<PAGE>

                                                                 EXHIBIT 10.3(b)

                         INFONET SERVICES CORPORATION
                         STOCK OPTION AWARD AGREEMENT

          This Agreement (this "Agreement"), dated as of ________________, is
made between INFONET SERVICES CORPORATION (the "Company") and _____________ (the
"Optionee").  All capitalized terms used herein that are not defined herein
shall have the respective meanings given to such terms in the Infonet Services
Corporation 1999 Stock Option Plan (the "Plan").  The terms and conditions of
the Plan, together with all defined terms included in the Plan are, by this
reference, incorporated in this Agreement as if set forth in this Agreement in
their entirety.

                             W I T N E S S E T H :
                             --------------------

     1.  Grant of Option.  Pursuant to the provisions of the Plan, the Company
         ---------------
hereby grants to the Optionee the right and option to purchase from the Company
(the "Option") all or any part of an aggregate of ______________ shares of the
Class B common stock of the Company (the "Stock").  The percentages listed below
of all shares of Stock purchased at any time in accordance with this Agreement
shall have a purchase price per share equal to the amount set forth below
opposite each such percentage:
<TABLE>
<CAPTION>

                  Percentage                     Price
                  -------------------------------------
                  <S>                            <C>



</TABLE>

          2.  Expiration.  The Option shall expire on
              ----------

          3.  Exercise of Option.  Subject to the other terms of this Agreement
              ------------------
and the Plan, the Option may be exercised on or after the dates indicated below,
in whole or in part, as to that percentage of the total  shares of Stock subject
to the Option as set forth below opposite each such date, plus any shares of
Stock as to which the Option could have been exercised previously, but was not
so exercised:


<TABLE>
<CAPTION>
                       Date                     Percentage
                       -----------------------------------
                      <S>                      <C>
</TABLE>
<PAGE>

          4.  Transferability.  The Option shall be personal to the Optionee and
              ---------------
shall not be transferable otherwise than by will or the laws of descent and
distribution, and is exercisable, during the lifetime of the Optionee, only by
him; provided, however, that, subject to the terms of the Plan, (a) the Option
may be exercised after the Optionee's death by the beneficiary most recently
named by the Optionee in a written designation thereof filed by the Optionee
with the Company, or, in lieu of any such surviving beneficiary, as designated
by the Optionee by will or by the laws of descent and distribution; (b) the
Option may be transferred by the Optionee during his lifetime to the Optionee's
alternate payee pursuant to a qualified domestic relations order, as defined by
the Code or Title I of the Employee Retirement Income Security Act of 1974, as
amended, or the rules and regulations thereunder; and (c) subject to such terms,
conditions and limitations as may be prescribed by the Committee, all or a
portion of the Option may be transferred by the Optionee to his spouse, child,
stepchild, grandchild, parent, grandparent, sibling, niece, nephew, mother-in-
law, father-in-law, son-in-law, daughter-in-law, brother-in-law or sister-in-
law, including adoptive relationships, or a trust or trusts for the exclusive
benefit of any such individuals and/or the Optionee, a partnership or limited
liability company in which any such individuals and/or the Optionee are the only
partners or members or a similar entity in the discretion of the Committee;
provided that (x) there may be no consideration for any such transfer and (y)
following any such transfer, the Option may not be subsequently transferred by
any transferee, otherwise than by will or by the laws of descent and
distribution; and provided further that, following any such transfer, the
provisions of paragraph 3 of this Agreement and Section 6(e) of the Plan shall
continue to be applied with respect to the Optionee and the Optionee's
Termination of Employment, and exercise of the Option by any transferee of the
Option shall continue at all times to be governed by such provisions.

          5.  No Rights as Stockholder.  Neither the Optionee nor any other
              ------------------------
person shall  become the beneficial owner of the shares of Stock subject to the
Option, nor have any rights to dividends or other rights as a shareholder with
respect to any such shares, until the Optionee has exercised the Option in
accordance with the provisions of the Plan.

          6.  No Right to Continued Employment.  The Option shall not confer
              --------------------------------
upon the Optionee any right to be retained in the service of the Company or a
Subsidiary, nor restrict in any way the right of the Company or any Subsidiary,
which right is hereby expressly reserved, to terminate his employment at any
time with or without cause.

          7.  Relationship with Plan.  Notwithstanding any provision herein to
              ----------------------
the contrary, the Option provides the Optionee with no greater rights or claims
than are specifically provided for under the Plan.

          8.  Compliance with Laws, Regulations, Etc.  The Option and the
              --------------------------------------
obligation of the Company to sell and deliver shares of Stock upon the exercise
thereof in accordance with the Plan shall be subject in all respects to (a) all
applicable Federal and state laws, rules and regulations and (b) any
registration, qualification, approvals or other requirements imposed by
<PAGE>

any government or regulatory agency or body. Moreover, the Option may not be
exercised if its exercise, or the receipt of shares of Stock pursuant thereto,
would be contrary to applicable law.

          9.  Investment Representation.  If at the time of exercise of all or
              -------------------------
part of the Option  the Stock is not registered under the Securities Act of
1933, as amended (the "Securities Act"), and/or there is no current prospectus
in effect under the Securities Act with respect to the Stock, the Optionee shall
execute, prior to the issuance of any shares of Stock to the Optionee by the
Company, an agreement (in such form as the Committee may specify) in which the
Optionee, among other things, represents, warrants and agrees that (a) the
Optionee (i) is purchasing or acquiring the shares acquired under this Agreement
for the Optionee's own account, for investment only and not with a view to the
resale or distribution thereof, (ii) has knowledge and experience in financial
and business matters, (iii) is capable of evaluating the merits and risks of
owning any shares of Stock purchased or acquired under this Agreement, and (iv)
is a person who is able to bear the economic risk of such ownership and (b) any
subsequent offer for sale or distribution of any of such shares shall be made
only pursuant to (i) a registration statement on an appropriate form under the
Securities Act, which registration statement has become effective and is current
with regard to the shares being offered or sold, or (ii) a specific exemption
from the registration requirements of the Securities Act, it being understood
that to the extent any such exemption is claimed, the Optionee shall, prior to
any offer for sale or sale of such shares, obtain a prior favorable written
opinion, in form and substance satisfactory to the Committee, from counsel for
or approved by the Committee, as to the applicability of such exemption thereto.

          10. Optionee Bound by Plan.  The Optionee hereby acknowledges receipt
              ----------------------
of a copy of the Plan and agrees to be bound by all of the terms and provisions
thereof, including the terms and provisions adopted after the granting of the
Option, but prior to the complete exercise hereof, subject to the last paragraph
of Section 14 of the Plan as in effect on the date hereof.

          11. Notices.  Any notice hereunder shall be in writing and if to the
              -------
Company shall be addressed to it at 2160 East Grand Avenue, El Segundo,
California 90245, Attention:  Mr. Ernest U. Gambaro, and if to the Optionee,
shall be addressed to him at the address set forth below his signature on the
signature page of this Agreement, subject to the right of either party to
designate at any time hereafter in writing some other address.

          12. Governing Law.  THE VALIDITY, INTERPRETATION, CONSTRUCTION AND
              -------------
PERFORMANCE OF THIS AGREEMENT SHALL BE GOVERNED BY THE LAWS OF THE STATE OF
CALIFORNIA APPLICABLE TO CONTRACTS EXECUTED AND TO BE PERFORMED ENTIRELY WITHIN
SUCH STATE, WITHOUT REGARD TO THE CONFLICT OF LAW PROVISIONS THEREOF.

          13. Severability.  If any of the provisions of this Agreement should
              ------------
be deemed unenforceable, the remaining provisions shall remain in full force and
effect.

          14. Modification.  Except as otherwise permitted by the Plan, this
              ------------
Agreement may not be modified or amended, nor may any provision hereof be
waived, in any way except in writing signed by the party against whom
enforcement thereof is sought.
<PAGE>

          15.  Counterparts.  This Agreement has been executed in two
               ------------
counterparts, each of which shall constitute one and the same instrument.

          16.  Previous Agreements.  It is hereby agreed and understood that any
               -------------------
stock option award agreements entered into by the parties hereto prior to the
date hereof under the Plan are hereby terminated and superseded and of no
further force or effect.

     IN WITNESS WHEREOF, Infonet Services Corporation has caused this Agreement
to be executed by a duly authorized officer and the Optionee has executed this
Agreement, both as of the day and year first above written.

                              INFONET SERVICES CORPORATION


                              By:__________________________________
                                 Name:
                                 Title:


                              _____________________________________

                              Address for Notices:
<PAGE>

<TABLE>
<CAPTION>

                                         NOTATIONS AS TO PARTIAL EXERCISE
=======================================================================================================================
    Date of         Number of Shares    Number of Shares of    Balance of Shares        Authorized          Notation
    Exercise      of Stock subject to    Stock delivered to    of Stock on Option       Signature             Date
                        Exercise              Optionee
-----------------------------------------------------------------------------------------------------------------------
<S>               <C>                   <C>                   <C>                   <C>                 <C>
-----------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------------------------------------

=======================================================================================================================
</TABLE>