<PAGE>   1
                                                                    EXHIBIT 10.3

                            INDEMNIFICATION AGREEMENT

         This Indemnification Agreement is entered into April 3, 2000 and
effective as of the 14th day of September, 1999 ("Agreement"), by and between
PetroQuest Energy, Inc., a Delaware corporation ("Company"), and Francisco A.
Garcia ("Indemnitee"):

         WHEREAS, highly competent persons have become more reluctant to serve
corporations as directors, executive officers or in other capacities unless they
are provided, with adequate protection through insurance or adequate
indemnification against inordinate risks of claims and actions against them
arising out of their service to, and activities on behalf of, the corporation;

         WHEREAS, the Board of Directors of the Company (the "Board") has
determined that, in order to attract and retain qualified individuals, the
Company will attempt to maintain on an ongoing basis, at its sole expense,
liability insurance to protect persons' serving the Company and its subsidiaries
from certain liabilities. Although the furnishing of such insurance has been a
customary and widespread practice among United States-based corporations and
other business enterprises, the Company believes that, given current market
conditions and trends, such insurance may be available to it in the future only
at higher premiums and with more exclusions. At the same time, directors,
officers and other persons in service to corporations or business enterprises
are being increasingly subjected to expensive and time-consuming litigation
relating to, among other things, matters that traditionally would have been
brought only against the corporation or business enterprise itself;

         WHEREAS, the uncertainties relating to such insurance and to
indemnification have increased the difficulty of attracting and retaining such
persons;

         WHEREAS, the Board has determined that the increased difficulty in
attracting and retaining such persons is detrimental to the best interests of
the Company's stockholders and that the Company should act to assure such
persons that there will be increased certainty of such protection in the future;

         WHEREAS, it is reasonable, prudent and necessary for the Company
contractually to obligate itself to indemnify such persons to the fullest extent
permitted by applicable law so that they will serve or continue to serve the
Company free from undue concern that they will not be so indemnified; and

         WHEREAS, indemnitee is willing to serve, continue to serve and to take
on additional service for or on behalf of the Company on the condition that he
be so indemnified;

         NOW, THEREFORE, in consideration of the premises and the covenants
contained herein, the Company and Indemnitee do hereby covenant and agree as
follows:



<PAGE>   2



         SECTION 1. Services by Indemnitee. Indemnitee agrees to serve as a
director/executive officer of the Company and, as mutually agreed by Indemnitee
and the Company, as a director, officer, employee, agent or fiduciary of other
corporations, partnerships, joint ventures, trusts or other enterprises
(including, without limitation, employee benefit plans). Indemnitee may at any
time and for any reason resign from any such position (subject to any other
contractual obligation or any obligation imposed by operation of law), in which
event the Company shall have no obligation under this Agreement to continue
Indemnitee in that position. This Agreement shall not be deemed an employment
contract between the Company (or any of its subsidiaries) and Indemnitee.
Indemnitee specifically acknowledges that Indemnitee's employment with the
Company (or any of its subsidiaries), if any, is at will, and the Indemnitee may
be discharged at any time for any reason, with or without cause, except as may
be otherwise provided in any written employment contract between Indemnitee and
the Company (or any of its subsidiaries), other applicable formal severance
policies duly adopted by the Board or, with respect to service as a director of
the Company, by the Company's Certificate of incorporation, Bylaws and the
General Corporation Law of the State of Delaware. Notwithstanding, the
foregoing, this Agreement shall continue in force after Indemnitee has ceased to
serve as an officer or director of the Company and no longer serves at the
request of the Company as a director, officer, employee or agent of the Company
or any subsidiary of the Company.

         SECTION 2. Indemnification--General. The Company shall indemnify, and
advance Expenses (as hereinafter defined) to, Indemnitee (a) as provided in this
Agreement and (b) to the fullest extent permitted by applicable law in effect on
the date hereof and as amended from time to time. The rights of Indemnitee
provided under the preceding sentence shall include, but shall not be limited
to, the rights set forth in the other Sections of this Agreement.

         SECTION 3. Proceedings Other than Proceedings by or in the Right of the
Company. Indemnitee shall be entitled to the rights of indemnification provided
in Section 2 and this Section 3 if, by reason of his Corporate Status (as
hereinafter defined), he is, or is threatened to be made, a party to or a
participant in any threatened, pending, or completed Proceeding (as hereinafter
defined), other than a Proceeding by or in the right of the Company. Pursuant to
this Section 3, the Company shall indemnify Indemnitee against, and shall hold
Indemnitee harmless from and in respect of, all Expenses, judgments, penalties,
fines (including excise taxes) and amounts paid in settlement (including all
interest, assessments and other charges paid or payable in connection with or in
respect of such Expenses, judgments, fines, penalties or amounts paid in
settlement) actually and reasonably incurred by him or on his behalf in
connection with such Proceeding or any claim, issue or matter therein, if he
acted in good faith and in a manner he reasonably believed to be in or not
opposed to the best interests of the Company and, with respect to any criminal
Proceeding, had no reasonable cause to believe his conduct was unlawful.

         SECTION 4. Proceedings by or in the Right of the Company. Indemnitee
shall be entitled to the rights of indemnification provided in Section 2 and
this Section 4 if, by reason of his Corporate Status, he is, or is threatened to
be made, a party to or a participant in any threatened, pending or completed
Proceeding brought by or in the right of the Company to procure a judgment in
its favor. Pursuant to this Section 4, the Company shall indemnify Indemnitee
against, and shall


                                       2
<PAGE>   3

hold Indemnitee harmless from and in respect of, all Expenses actually and
reasonably incurred by him or on his behalf in connection with, and any amounts
paid in settlement of, such Proceeding if he acted in good faith and in a manner
he reasonably believed to be in or not opposed to the best interests of the
Company. Notwithstanding the foregoing, no indemnification against such Expenses
shall be made in respect of any claim, issue or matter in such Proceeding as to
which Indemnitee shall have been adjudged to be liable to the Company if
applicable law prohibits such indemnification; provided, however, if applicable
law so permits, indemnification against such Expenses shall nevertheless be made
by the Company in such event if and only to the extent that the Court of
Chancery of the State of Delaware, or the court in which such Proceeding shall
have been brought or is pending, shall determine.

         SECTION 5. Indemnification for Expenses of a Party Who Is Wholly or
Partly Successful. Notwithstanding any other provision of this Agreement, to the
extent that Indemnitee is, by reason of his Corporate Status, a party to (or a
participant in) and is successful, on the merits or otherwise, in defense of any
Proceeding, he shall be indemnified against all Expenses actually and reasonably
incurred by him or on his behalf in connection therewith. If Indemnitee is not
wholly successful in defense of such Proceeding but is successful, on the merits
or otherwise, as to one or more but less than all claims, issues or matters in
such Proceeding, the Company shall indemnify Indemnitee against all Expenses
actually and reasonably incurred by him or on his behalf in connection with each
successfully resolved claim, issue or matter. For purposes of this Section and
without limitation, the termination of any claim, issue or matter in such a
Proceeding by dismissal, with or without prejudice, shall be deemed to be a
successful result as to such claim, issue or matter.

         SECTION 6. Indemnification for Expenses as a Witness. Notwithstanding
any other provision of this Agreement, to the extent that Indemnitee is, by
reason of his Corporate Status, a witness in any Proceeding to which Indemnitee
is not a party, he shall be indemnified against all Expenses actually and
reasonably incurred by him or on his behalf in connection therewith.

         SECTION 7. Advancement of Expenses. The Company shall advance all
reasonable Expenses incurred by or on behalf of Indemnitee in connection with
any Proceeding within ten (10) days after the receipt by the Company of a
statement or statements from Indemnitee requesting such advance or advances from
time to time, whether prior to or after final disposition of such Proceeding.
Such statement or statements shall reasonably evidence the Expenses incurred by
Indemnitee and shall include or be preceded or accompanied by an undertaking by
or on behalf of Indemnitee to repay any Expenses advanced if it ultimately shall
be determined, in accordance with this Agreement, that Indemnitee is not
entitled to be indemnified against such Expenses.

         SECTION 8. Procedure for Determination of Entitlement to
Indemnification.

         (a) To obtain indemnification under this Agreement, Indemnitee shall
submit to the Company a written request, including therein or therewith such
documentation and information as is reasonably available to Indemnitee and is
reasonably necessary to determine whether and to what extent Indemnitee is
entitled to indemnification. The Secretary of the Company shall, promptly upon
receipt of such a request for indemnification, advise the Board in writing that
Indemnitee has requested indemnification.



                                       3
<PAGE>   4

         (b) On written request by Indemnitee for indemnification pursuant to
the first sentence of Section 8(a), a determination, if required by applicable
law, with respect to Indemnitee's entitlement thereto shall be made in the
specific case: (i) if a Change in Control (as hereinafter defined) shall have
occurred within two (2) years prior to the date of such written request, by
Independent Counsel (as hereinafter defined) in a written opinion to the Board,
a copy of which shall be delivered to Indemnitee; or (ii) if a Change of Control
shall not have occurred within two (2) years prior to the date of such written
request, (A) by a majority vote of the Disinterested Directors (as hereinafter
defined), even though less than a quorum of the Board, or (B) if there are no
such Disinterested Directors, or if such Disinterested Directors so direct, by
Independent Counsel in a written opinion to the Board, a copy of which shall be
delivered to Indemnitee; and, if it is so determined that Indemnitee is entitled
to indemnification, payment to Indemnitee shall be made within ten (10) days
after such determination. Indemnitee shall cooperate with the person, persons or
entity making such determination with respect to Indemnitee's entitlement to
indemnification, including providing to such person, persons or entity on
reasonable advance request any documentation or information which is not
privileged or otherwise protected from disclosure and which is reasonably
available to Indemnitee and reasonably necessary to such determination. Any
costs or expenses (including attorneys' fees and disbursements) incurred by
Indemnitee in so cooperating with the person, persons or entity making such
determination shall be borne by the Company (irrespective of the determination
as to Indemnitee's entitlement to indemnification) and the Company hereby
indemnifies and agrees to hold Indemnitee harmless therefrom.

         (c) In the event the determination of entitlement to indemnification is
to be made by Independent Counsel pursuant to Section 8(b), the Independent
Counsel shall be selected as provided in this Section 8(c). If a Change of
Control shall not have occurred within two (2) years prior to the date of
Indemnitee's written request for indemnification pursuant to Section 8(a), the
Independent Counsel shall be selected by the Board, and the Company shall give
written notice to Indemnitee advising him of the identity of the Independent
Counsel so selected. If a Change of Control shall have occurred within two (2)
years prior to the date of Indemnitee's written request for indemnification
pursuant to Section 8(a), the Independent Counsel shall be selected by
Indemnitee (unless Indemnitee shall request that such selection be made by the
Board, in which event the preceding sentence shall apply), and Indemnitee shall
give written notice to the Company advising it of the identity of the
Independent Counsel so selected in either event, Indemnitee or the Company, as
the case may be, may, within ten (10) days after such written notice of
selection shall have been given, deliver to the Company or to Indemnitee, as the
case may be, a written objection to such selection. Such objection may be
asserted only on the ground that the Independent Counsel so selected does not
meet the requirements of "Independent Counsel" as defined in section 17, and the
objection shall set forth with particularity the factual basis of such
assertion. If such written objection is so made and substantiated, the
Independent Counsel so selected may not serve as Independent Counsel unless and
until such objection is withdrawn or a court has determined that such objection
is without merit. If, within twenty (20) days after submission by Indemnitee of
a written request for indemnification pursuant to Section 8(a), no Independent
Counsel shall have been selected and not objected to, either the Company or
Indemnitee may petition the Court of Chancery or other court of competent
jurisdiction for resolution of any objection which shall have been made by the
Company or Indemnitee to the other's selection of Independent Counsel and/or for
the appointment as Independent Counsel of a person selected by the petitioned
court or by such other



                                       4
<PAGE>   5

person as the petitioned court shall designate, and the person with respect to
whom all objections are so resolved or the person so appointed shall act as
Independent Counsel under Section 8(b). The Company shall pay any and all
reasonable fees and expenses of Independent Counsel incurred by such Independent
Counsel in connection with acting pursuant to Section 8(b), and the Company
shall pay all reasonable fees and expenses incident to the procedures of this
Section 8(c), regardless of the manner in which such Independent Counsel was
selected and appointed. If (i) Independent Counsel does not make any
determination respecting Indemnitee's entitlement to indemnification hereunder
within ninety (90) days after receipt by the Company of a written request
therefor and (ii) any judicial proceeding or arbitration pursuant to Section
10(a)(iii) hereof is then commenced, Independent Counsel shall be discharged and
relieved of any further responsibility in such capacity (subject to the
applicable standards of professional conduct then prevailing).

         SECTION 9. Presumptions and Effect of Certain Proceedings.

         (a) In making a determination with respect to entitlement to
indemnification hereunder, the Person, Persons or entity making such
determination shall presume that Indemnitee is entitled to indemnification under
this Agreement if Indemnitee has submitted a request for indemnification in
accordance with Section 8(a), and the Company shall have the burden of proof to
overcome that presumption in connection with the making by any person, persons
or entity of any determination contrary to that presumption.

         (b) The termination of any Proceeding or of any claim, issue or matter
therein, by judgment, order, settlement or conviction, or on a plea of nolo
contendere or its equivalent, shall not (except as otherwise expressly provided
in this Agreement) of itself adversely affect the right of Indemnitee to
indemnification or create a presumption that Indemnitee did not act in good
faith and in a manner which he reasonably believed to be in or not opposed to
the best interests of the Company or, with respect to any criminal Proceeding,
that Indemnitee had reasonable cause to believe that his conduct was unlawful.

         (c) Any action taken by Indemnitee in connection with any employee
benefit plan shall, if taken in good faith by Indemnitee and in a manner
Indemnitee reasonably believed to be in the interest of the participants in or
beneficiaries of that plan, be deemed to have been taken in a manner "not
opposed to the best interests of the Company" for all purposes of this
Agreement.

         SECTION 10. Remedies of Indemnitee.

         (a) In the event that (i) a determination is made pursuant to Section 8
that Indemnitee is not entitled to indemnification hereunder, (ii) advancement
of Expenses is not timely made pursuant to Section 7, (iii) Independent Counsel
is to determine Indemnitee's entitlement to indemnification hereunder, but does
not make that determination within ninety (90) days after receipt by the Company
of the request for that indemnification, (iv) payment of indemnification is not
made pursuant to section 5 or 6 within ten (10) days after receipt by the
Company of a written request therefor or (v) payment of indemnification is not
made within ten (10) days after a determination has been made that Indemnitee is
entitled to indemnification, Indemnitee shall be entitled to an adjudication
from the Court of Chancery of his entitlement to such indemnification or
advancement


                                       5
<PAGE>   6


of Expenses. Alternatively, Indemnitee, at his option, may seek an award in
arbitration to be conducted by a single arbitrator pursuant to the Commercial
Arbitration Rules of the American Arbitration Association. Indemnitee shall
commence such Proceeding seeking an adjudication or an award in arbitration
within one hundred eighty (180) days following the date on which Indemnitee
first has the right to commence such proceeding pursuant to this Section 10(a);
provided, however, that the foregoing clause shall not apply in respect of a
proceeding brought by Indemnitee to enforce his rights under Section 5.

         (b) In the event that a determination shall have been made pursuant to
Section 8(b) that Indemnitee is not entitled to indemnification, any judicial
proceeding or arbitration commenced pursuant to this Section 10 shall be
conducted in all respects as a de novo trial, or arbitration, on the merits and
Indemnitee shall not be prejudiced by reason of that adverse determination. In
any judicial proceeding or arbitration commenced pursuant to this section 10,
the Company shall have the burden of proving that Indemnitee is not entitled to
indemnification or advancement of Expenses, as the case may be.

         (c) If a determination shall have been made pursuant to Section 8(b)
that Indemnitee is entitled to indemnification, the Company shall be bound by
such determination in any judicial proceeding or arbitration commenced pursuant
to this Section 10, absent (i) a misstatement by Indemnitee of a material fact,
or an omission by Indemnitee of a material fact necessary to make Indemnitee's
statement not materially misleading, in connection with the request for
indemnification, or (ii) a prohibition of such indemnification under applicable
law.

         (d) In the event that Indemnitee, pursuant to this Section 10, seeks a
judicial adjudication of or an award in arbitration to enforce his rights under,
or to recover damages for breach of, this Agreement, Indemnitee shall be
entitled to recover from the Company, and shall be indemnified by the Company
against, any and all expenses (of the types described in the definition of
Expenses in Section 17) actually and reasonably incurred by him in such judicial
adjudication or arbitration, but only if he prevails therein. If it shall be
determined in said judicial adjudication or arbitration that Indemnitee is
entitled to receive part but not all of the indemnification or advancement of
expenses sought, the expenses incurred by Indemnitee in connection with such
judicial adjudication or arbitration shall be appropriately prorated.

         SECTION 11. Non-Exclusivity; Survival of Rights; Insurance;
Subrogation.

         (a) The rights of indemnification and to receive advancement of
Expenses as provided by this Agreement shall not be deemed exclusive of any
other rights to which Indemnitee may at any time be entitled under applicable
law, the Certificate of Incorporation, the Bylaws, any agreement, a vote of
stockholders or a resolution of directors, or otherwise. No amendment,
alteration or repeal of this Agreement or of any provision hereof shall limit or
restrict any right of Indemnitee under this Agreement in respect of any action
taken or omitted by such Indemnitee in his Corporate Status prior to such
amendment, alteration or repeal. To the extent that a change in Delaware law
(whether by statute or judicial decision) permits greater indemnification by
agreement than would be afforded currently under this Agreement, it is the
intent of the parties hereto that Indemnitee shall enjoy by this Agreement the
greater benefits so afforded by such change.



                                       6
<PAGE>   7

         (b) To the extent that the Company maintains an insurance policy or
policies providing liability insurance for directors, officers, employees, or
agents of the Company or of any other corporation, partnership, joint venture,
trust, employee benefit plan or other enterprise which such person serves at the
request of the Company, Indemnitee shall be covered by such policy or policies
in accordance with its or their terms to the maximum extent of the coverage
available for any such director, Officer, employee or agent under such policy or
policies.

         (c) In the event of any payment under this Agreement, the Company shall
be subrogated to the extent of such payment to all the rights of recovery of
Indemnitee, who shall execute all papers required and take all action necessary
to secure such rights, including execution of such documents as are necessary to
enable the Company to bring suit to enforce such rights.

         (d) The Company shall not be liable under this Agreement to make any
payment of amounts otherwise indemnifiable hereunder if and to the extent that
Indemnitee has otherwise actually received such payment under any insurance
policy, contract, agreement or otherwise.

         (e) The Company's obligation to indemnify or advance Expenses hereunder
to Indemnitee with respect to Indemnitee's service at the request of the Company
as a director, officer, employee or agent of any other corporation, partnership,
joint venture, trust, employee benefit plan or other enterprise shall be reduced
by any amount Indemnitee has actually received as indemnification or advancement
of Expenses from such other corporation, partnership, joint venture, trust,
employee benefit plan or other enterprise.

         SECTION 12. Duration of Agreement. This Agreement shall continue until
and terminate upon the later of: (a) ten (10) years after the date that
Indemnitee shall have ceased to serve as a director or officer of the Company or
of any other corporation, partnership, joint venture, trust, employee benefit
plan or other enterprise which Indemnitee served on behalf of the Company; or
(b) the final termination of any Proceeding then pending in respect of which
Indemnitee is granted rights of indemnification or advancement of expenses
hereunder and of any Proceeding commenced by Indemnitee pursuant to Section 10
relating thereto. This Agreement shall be binding upon the Company and its
successors and assigns and shall inure to the benefit of Indemnitee and his
spouse (if Indemnitee resides in Texas or another community property state),
heirs, executors and administrators, and this Agreement does not, and shall not
be construed to confer any rights on any person that is not a party to this
Agreement, other than Indemnitee's spouse, and his heirs, executors and assigns.

         SECTION 13. Severability. If any provision or provisions of this
Agreement shall be held to be invalid, illegal or unenforceable for any reason
whatsoever: (a) the validity, legality and enforceability of the remaining
provisions of this Agreement (including, without limitation, each portion of any
Section of this Agreement containing any such provision held to be invalid,
illegal or unenforceable which is not itself invalid, illegal or unenforceable)
shall not in any way be affected or impaired thereby; (b) such provision or
provisions shall be deemed reformed to the extent necessary to conform to
applicable law and to give the maximum effect to the intent of the parties
hereto; and (c) to the fullest extent possible, the provisions of this Agreement
(including, without limitation, each portion of any Section of this Agreement
containing any such provision held to be


                                       7
<PAGE>   8

invalid, illegal or unenforceable which is not itself invalid, illegal or
unenforceable) shall be construed so as to give effect to the intent manifested
thereby.

         SECTION 14. Exception to Right of Indemnification or Advancement of
Expenses. Notwithstanding any other provision hereof, Indemnitee shall not be
entitled to indemnification or advancement of Expenses under this Agreement with
respect to any Proceeding brought by Indemnitee or any claim therein prior to a
Change in Control, unless the bringing of such Proceeding or making of such
claim shall have been approved by the Board of Directors.

         SECTION 15. Identical Counterparts. This Agreement may be executed in
one or more counterparts by means of original or facsimile signatures, each of
which shall for all purposes be deemed to be an original but all of which
together shall constitute one and the same Agreement. Only one such counterpart
signed by the party against whom enforceability is sought needs to be produced
to evidence the existence of this Agreement.

         SECTION 16. Headings. The headings of the Sections hereof are inserted
for convenience only and shall not be deemed to constitute part of this
Agreement or to affect the construction thereof.

         SECTION 17. Definitions. For purposes of this Agreement:

                  (a) "Acquiring Person" means any Person who or which, together
         with all Affiliates and Associates of such Person, is or are the
         Beneficial Owner of twenty-five percent (25%) or more of the shares of
         Common Stock then outstanding, but does not include any Exempt Person;
         provided, however, that a Person shall not be or become an Acquiring
         Person if such Person, together with its Affiliates and Associates,
         shall become the Beneficial Owner of twenty-five percent (25%) or more
         of the shares of Common Stock then outstanding solely as a result of a
         reduction in the number of shares of Common Stock outstanding due to
         the repurchase of Common Stock by the Company, unless and until such
         time as such Person or any Affiliate or Associate of such Person shall
         purchase or otherwise become the Beneficial Owner of additional shares
         of Common Stock constituting one percent (1%) or more of the then
         outstanding shares of Common Stock or any other Person (or Persons) who
         is (or collectively are) the Beneficial Owner of shares of Common Stock
         constituting one percent (1%) or more of the then outstanding shares of
         Common Stock shall become an Affiliate or Associate of such Person,
         unless, in either such case, such Person, together with all Affiliates
         and Associates of such Person, is not then the Beneficial Owner of
         twenty-five percent (25%) or more of the shares of Common Stock then
         outstanding.

                  (b) "Affiliate" has the meaning ascribed to that term in
         Exchange Act Rule 12b-2.

                  (c) "Associate" means, with reference to any Person, (i) any
         corporation, firm, partnership, association, unincorporated
         organization or other entity (other than the Company or a subsidiary of
         the Company) of which that Person is an officer or



                                       8
<PAGE>   9

         general partner (or officer or general partner of a general partner) or
         is, directly or indirectly, the Beneficial owner of 10% or more of any
         class of its equity securities, (ii) any trust or other estate in which
         that Person has a substantial beneficial interest or for or of which
         that Person serves as trustee or in a similar fiduciary capacity and
         (iii) any relative or spouse of that Person, or any relative of that
         spouse, who has the same home as that Person.

                  (d) A specified Person is deemed the "Beneficial Owner" of,
         and is deemed to "beneficially own," any securities:

                           (i) of which that Person or any of that Person's
                  Affiliates or Associates, directly or indirectly, is the
                  "beneficial owner" (as determined pursuant to Exchange Act
                  Rule 13d-3) or otherwise has the right to vote or dispose of,
                  including pursuant to any agreement, arrangement or
                  understanding (whether or not in writing); provided, however,
                  that a Person shall not be deemed the "Beneficial Owner" of,
                  or to "beneficially own," any security under this subparagraph
                  as a result of an agreement, arrangement or understanding to
                  vote that security if that agreement, arrangement or
                  understanding: (A) arises solely from a revocable proxy or
                  consent given in response to a public (that is, not including
                  a solicitation exempted by Exchange Act Rule 14a-2(b)(2))
                  proxy or consent solicitation made pursuant to, and in
                  accordance with, the applicable provisions of the Exchange
                  Act; and (B) is not then reportable by such Person on Exchange
                  Act Schedule 13D (or any comparable or successor report);

                           (ii) which that Person or any of that Person's
                  Affiliates or Associates, directly or indirectly, has the
                  right or obligation to acquire (whether that right or
                  obligation is exercisable or effective immediately or only
                  after the passage of time or the occurrence of an event)
                  pursuant to any agreement, arrangement or understanding
                  (whether or not in writing) or on the exercise of conversion
                  rights, exchange rights, other rights, warrants or options, or
                  otherwise; provided, however, that a Person shall not be
                  deemed the "Beneficial Owner" of, or to "beneficially own,"
                  securities tendered pursuant to a tender or exchange offer
                  made by that Person or any of that Person's Affiliates or
                  Associates until those tendered securities are accepted for
                  purchase or exchange; or

                           (iii) which are beneficially owned, directly or
                  indirectly, by (A) any other Person (or any Affiliate or
                  Associate thereof) with which the specified Person or any of
                  the specified Person's Affiliates or Associates has any
                  agreement, arrangement or understanding (whether or not in
                  writing) for the purpose of acquiring, holding, voting (except
                  pursuant to a revocable proxy or consent as described in the
                  proviso to subparagraph (i) of this definition) or disposing
                  of any voting securities of the Company or (B) any group (as
                  that


                                       9
<PAGE>   10

                  term is used in Exchange Act Rule 13d-5(b)) of which that
                  specified Person is a member;

PROVIDED, HOWEVER, that nothing in this definition shall cause a Person engaged
in business as an underwriter of securities to be the "Beneficial Owner" of, or
to "beneficially own," any securities acquired through such Person's
participation in good faith in a firm commitment underwriting until the
expiration of forty (40) days after the date of that acquisition. For purposes
of this Agreement, "voting" a security shall include voting, granting a proxy,
acting by consent, making a request or demand relating to corporate action
(including, without limitation, calling a stockholder meeting) or otherwise
giving an authorization (within the meaning of Section 14(a) of the Exchange
Act) in respect of such security.

                  (e) "Change of Control" means the occurrence of any of the
         following events that occurs after the effective date of this
         Agreement: (i) any Person becomes an Acquiring Person; (ii) at any time
         the then Continuing Directors cease to constitute a majority of the
         members of the Board; (iii) a merger of the Company with or into, or a
         sale by the Company of its properties and assets substantially as an
         entirety to, another Person occurs and, immediately after that
         occurrence, any Person, other than an Exempt Person, together with all
         Affiliates and Associates of such Person, shall be the Beneficial Owner
         of twenty-five percent (25%) or more of the total voting power of the
         then outstanding Voting Shares of the Person surviving that transaction
         (in the case or a merger or consolidation) or the Person acquiring
         those properties and assets substantially as an entirety.

                  (f) "Common Stock" means the common stock, par value $.001 per
         share, of the Company.

                  (g) "Continuing Director" means at any time any individual who
         then (i) is a member of the Board and was a member of the Board as of
         the effective date of this Agreement or whose nomination for his first
         election, or that first election, to the Board following that date was
         recommended or approved by a majority of the then Continuing Directors
         (acting separately or as a part of any action taken by the Board or any
         committee thereof) and (ii) is not an Acquiring Person, an Affiliate or
         Associate of an Acquiring Person or a nominee or representative of an
         Acquiring Person or of any such Affiliate or Associate.

                  (h) "Corporate Status" describes the status of a Person who is
         or was a director, officer, employee or agent of the Company or of any
         other corporation, partnership, joint venture, trust, employee benefit
         plan or other enterprise which such person is or was serving at the
         request of the Company. For purposes of this Agreement, "serving at the
         request of the Company" includes any service by Indemnitee which
         imposes duties on, or involves services by, Indemnitee with respect to
         any employee benefit plan or its participants or beneficiaries.



                                       10
<PAGE>   11

                  (i) "Court of Chancery" means the Court of Chancery of the
         State of Delaware.

                  (j) "Disinterested Director" means a director of the Company
         who is not and was not a party to the Proceeding in respect of which
         indemnification is sought by Indemnitee hereunder.

                  (k) "Exchange Act" means the Securities Exchange Act of 1934,
         as amended.

                  (l) "Exempt Person" means (i), (A) the Company, any subsidiary
         of the Company, any employee benefit plan of the Company or of any
         subsidiary of the Company and (B) any Person organized, appointed or
         established by the Company for or pursuant to the terms of any such
         plan or for the purpose of funding any such plan or funding other
         employee benefits for employees of the Company or any subsidiary of the
         Company and (ii) Indemnitee, any Affiliate or Associate of Indemnitee
         or any group (as that term is used in Exchange Act Rule 13d-5(b)) of
         which Indemnitee or any Affiliate or Associate of Indemnitee is a
         member.

                  (m) "Expenses" include all attorneys' fees, retainers, court
         costs, transcript costs, fees of experts, witness fees, travel
         expenses, duplicating costs, printing and binding costs, telephone
         charges, postage, delivery service fees, all other disbursements or
         expenses of the types customarily incurred in connection with
         prosecuting, defending, preparing to prosecute or defend,
         investigating, being or preparing to be a witness in, or otherwise
         participating in, a Proceeding and all interest or finance charges
         attributable to any thereof. Should any payments by the Company under
         this Agreement be determined to be subject to any federal, state or
         local income or excise tax, "Expenses" also shall include such amounts
         as are necessary to place Indemnitee in the same after-tax position
         (after giving effect to all applicable taxes) he would have been in had
         no such tax been determined to apply to such payments.

                  (n) "Independent Counsel" means a law firm, or a member of a
         law firm, that is experienced in matters of corporation law and neither
         presently is, nor in the past five (5) years has been, retained to
         represent: (i) the Company, its Affiliates or Indemnitee in any matter
         material to either such party; or (ii) any other Party to the
         Proceeding giving rise to a claim for indemnification hereunder.
         Notwithstanding the foregoing. the term "Independent Counsel" shall not
         include any person who, under the applicable standards of professional
         conduct then prevailing, would have a conflict of interest in
         representing either the Company or Indemnitee in an action to determine
         Indemnitee's rights under this Agreement.

                  (o) "Person" means any natural person, sole proprietorship,
         corporation, partnership of any kind having a separate legal status,
         limited liability company, business trust, unincorporated organization
         or association, mutual company, joint


                                       11
<PAGE>   12

         stock company, joint venture, estate, trust, union or employee
         organization or governmental authority.

                  (p) "Proceeding" includes any action, suit, alternate dispute
         resolution mechanism, hearing or any other proceeding, whether civil,
         criminal, administrative, arbitrative, investigative or mediative, any
         appeal in any such action, suit, alternate dispute resolution
         mechanism, hearing or other proceeding and any inquiry or investigation
         that could lead to any such action, suit, alternate dispute resolution
         mechanism, hearing or other proceeding, except one (i) initiated by an
         Indemnitee pursuant to Section 10 to enforce his rights hereunder or
         (ii) pending on or before the date of this Agreement.

                  (q) "Voting Shares" means: (i) in the case of any corporation,
         stock of that corporation of the class or classes having general voting
         power under ordinary circumstances to elect a majority of that
         corporation's board of directors; and (ii) in the case of any other
         entity, equity interests of the class or classes having general voting
         power under ordinary circumstances equivalent to the Voting Shares of a
         corporation.

         SECTION 18. Modification and Waiver. No supplement, modification or
amendment of this Agreement shall be binding unless executed in writing by both
of the parties hereto. No waiver of any of the provisions of this Agreement
shall be deemed or shall constitute a waiver of any other provisions hereof
(whether or not similar) nor shall such waiver constitute a continuing waiver.

         SECTION 19. Notice by Indemnitee. Indemnitee agrees promptly to notify
the Company in writing upon being served with any summons, citation, subpoena,
complaint, indictment, information or other document relating to any Proceeding
or matter which may be subject to indemnification or advancement of Expenses
covered hereunder; provided, however, failure to give such notice shall not
deprive Indemnitee of his rights to indemnification and advancement of Expenses
under this Agreement unless the Company is actually and materially prejudiced
thereby.

         SECTION 20. Notices. All notices, requests, demands and other
communications hereunder shall be in writing and shall be deemed to have been
duly given if (a) delivered by hand and receipted for by the party to whom said
notice or other communication shall have been directed or (b) mailed by
certified or registered mail with postage prepaid, on the third (3rd) business
day after the date on which it is so mailed:

                (a)  If to Indemnitee, to:  Francisco A. Garcia
                                            881 Ocean Drive, Suite 20-F
                                            Key Biscayne, Florida 33149





                                       12
<PAGE>   13


                 (b) If to the Company, to: PetroQuest Energy, Inc.
                                            625 E. Kaliste Saloom Rd., Suite 400
                                            Lafayette, Louisiana 70508
                                            Attention: Corporate Secretary

or to such other address as may have been furnished to Indemnitee by the Company
or to the Company by Indemnitee, as the case way be.

         SECTION 21. Contribution. To the fullest extent permissible under
applicable law, if the indemnification provided for in this Agreement is
unavailable to Indemnitee for any reason whatsoever, the Company, in lieu of
indemnifying Indemnitee, shall contribute to the amount incurred by Indemnitee,
whether for judgments, fines, penalties, excise taxes, amounts paid or to be
paid in settlement and/or for Expenses, in connection with any claim relating to
an indemnifiable event under this Agreement, in such proportion as is deemed
fair and reasonable in light of all the circumstances of such Proceeding in
order to reflect: (a) the relative benefits received by the Company and
Indemnitee as a result of the event(s) and/or transaction(s) giving cause to
such Proceeding; and/or (b) the relative fault of the Company (and its
directors, officers, employees and agents) and Indemnitee in connection with
such event(s) and/or transaction(s).

         SECTION 22. Governing Law; Submission to Jurisdiction. This Agreement
and the legal relations among the parties shall be governed by, and construed
and enforced in accordance with, the laws of the State of Delaware, without
regard to its conflict of laws rules. Except with respect to any arbitration
commenced by Indemnitee pursuant to Section 10(a), the Company and Indemnitee
hereby irrevocably and unconditionally (a) agree that any action or proceeding
arising out of or in connection with this Agreement shall be brought only in the
Court of Chancery and not in any other state or federal court in the United
States of America or any court in any other country, (b) consent to submit to
the exclusive jurisdiction of the Court of Chancery for purposes of any action
or proceeding arising out of or in connection with this Agreement, (c) waive any
objection to the laying of venue of any such action or proceeding in the Court
of Chancery, and (d) waive, and agree not to plead or to make, any claim that
any such action or proceeding brought in the Court of Chancery has been brought
in an improper or otherwise inconvenient forum.

         SECTION 23. Miscellaneous. Use of the masculine pronoun shall be deemed
to include usage of the feminine pronoun where appropriate. When used in this
Agreement, the words "herein," "hereof" and words of similar import shall refer
to this Agreement as a whole and not to any provision of this Agreement, and the
word "Section" refers to a Section of this Agreement, unless otherwise
specified.





                                       13
<PAGE>   14




         IN WITNESS WHEREOF, the parties hereto have executed this Agreement on
the day and year first above written.

                             PETROQUEST ENERGY, INC.



                             /s/ Charles T. Goodson
                             -------------------------------------
                             Charles T. Goodson,
                             President and Chief Executive Officer

                                            INDEMNITEE



                             /s/ Francisco A. Garcia
                             -------------------------------------
                             Francisco A. Garcia



                                       14