<PAGE>   1
                                                                   EXHIBIT 10.34


                             FIRST AMENDMENT TO THE
                               ROUGE STEEL COMPANY
                              STOCK INCENTIVE PLAN

             (As last Amended and Restated Effective July 30, 1997)

         WHEREAS, Rouge Industries, Inc., a Delaware corporation (the
"Company"), sponsors the Rouge Steel Company Stock Incentive Plan (as last
amended and restated effective July 30, 1997) (the "Plan"); and

         WHEREAS, the Company, by action of its Compensation Committee, desires
to amend the Plan.

         NOW, THEREFORE, the Company hereby amends the Plan, effective December
2, 1999, as follows:

         1.     A new subsection g. shall be added to Section 6.A.3, effective
December 2, 1999, to read in its entirety as follows:

                "g.    Notwithstanding the terms of any Option Agreement, but
         subject to the other provisions of this Section 6, in the event of the
         occurrence of a Change in Control, as defined herein, prior to an
         Optionee's retirement, disability, termination of employment or death,
         all outstanding Options shall become fully vested and exercisable.

                       For purposes of this Plan, "Change in Control" means,
         subject to the last paragraph of this subsection, the occurrence of any
         of the following events:

                       (1) The Company or Rouge Steel Company is merged,
                consolidated or reorganized into or with another corporation or
                other legal person, and as a result of such merger,
                consolidation or reorganization less than 55% of the combined
                voting power of the then-outstanding Voting Stock of such
                corporation or person immediately after such transaction are
                held in the aggregate by the Company or Rouge Steel Company or
                by the holders of Voting Stock of the Company immediately prior
                to such transaction;


                       (2) The Company or Rouge Steel Company sells or transfers
                all or substantially all of its assets to another corporation or
                other legal person, and as a result of such sale or transfer
                less than 55% of the combined voting power of the

                                      -1-
<PAGE>   2

                then-outstanding Voting Stock of such corporation or other legal
                person immediately after such sale or transfer is held in the
                aggregate by the Company or Rouge Steel Company or by the
                holders of Voting Stock of the Company immediately prior to such
                sale or transfer;

                       (3) The Company files a report or proxy statement with
                the Securities and Exchange Commission pursuant to the
                Securities Exchange Act of 1934 disclosing in response to Form
                8-K or Schedule 14A (or any successor schedule, form or report
                or item therein) that a change in control of the Company or
                Rouge Steel Company will occur in the future pursuant to a
                then-existing contract or transaction which when consummated
                would be a Change in Control determined without regard to this
                subsection (3);

                       (4) If, during any period of two (2) consecutive years,
                individuals who at the beginning of any such period constitute
                the directors of the Company cease for any reason to constitute
                at least a majority thereof; provided, however, that for
                purposes of this subsection (4), each director who is first
                elected, or first nominated for election by the Company's
                stockholders, by a vote of at least two-thirds of the directors
                of the Company (or a committee thereof) then still in office who
                were directors of the Company at the beginning of any such
                period will be deemed to have been a director of the Company at
                the beginning of such period; or

                       (5) Unless otherwise determined by a majority vote of the
                Board of Directors of the Company in the case of a corporate
                structure reorganization, the shareholders of the Company
                approve, pursuant to applicable state law requirements, a
                complete liquidation or dissolution of the Company or Rouge
                Steel Company.

                       Notwithstanding the foregoing provisions of subparagraph
         (3) above, unless otherwise determined in a specific case by a majority
         vote of the Board of Directors of the Company, a "Change in Control"
         shall not be deemed to have occurred for purposes of subparagraph (3)
         above solely because the Company, a subsidiary, or any
         Company-sponsored employee stock ownership plan or any other employee
         benefit plan of the Company or any subsidiary either files or becomes
         obligated to file a report or a proxy statement under or in response to
         Schedule 13D, Schedule 14D-1, Form 8-K or Schedule 14A (or any
         successor schedule, form or report or item therein) under the
         Securities Exchange Act of 1934 disclosing beneficial ownership by it
         of shares of Voting Stock, whether in excess of 20% or otherwise, or
         because the Company reports that a Change in Control of the Company has
         occurred or will occur in the future by reason of such beneficial
         ownership.


                       For purposes of this Article, "Voting Stock" means
         securities entitled to vote generally in the election of directors.

                                      -2-


<PAGE>   3


                       Notwithstanding anything to the contrary herein, a
         "Change in Control" shall not be deemed to have occurred solely as a
         result of a transfer of stock of the Company by Worthington Industries,
         Inc., or any of its affiliates or shareholders, to any lender pursuant
         to the amortization of one or more certain debt-in-exchange-for-capital
         loans between such parties which are referred to as "DECS" and which
         are evidenced by exchangeable notes due March 1, 2000. However, this
         paragraph shall not prohibit the occurrence of a "Change In Control"
         event if subsequent transactions would otherwise result in the
         occurrence of a "Change In Control" event pursuant to this subsection."

         2.     The phrase "Compensation Committee" in Section 12 is deleted and
replaced with the phrase "Committee."

         3.     Except as amended by this First Amendment, the terms of the Plan
shall remain in full force and effect.

         IN WITNESS WHEREOF, the Company has adopted this First Amendment as of
the 22nd day of December, 1999.


ATTEST:                             ROUGE INDUSTRIES, INC.



/s/ Martin Szymanski                By: /s/ William E. Hornberger
------------------------------          ---------------------------------
Secretary                                       William E. Hornberger
                                    Its:        Senior Vice President
                                        ---------------------------------

                                      -3-