This paper investigates strategic production selections in scenarios of credit sharing between cooperative fuel vehicle (FV) automakers and new energy vehicle (NEV) automakers under the dual-credit policy. Three coopetition production strategies are formulated: the simultaneous production strategy, the FV priority production strategy, and the NEV priority production strategy. On the basis of these three production strategies, this study examines the optimal strategy for both parties in scenarios of no credit sharing, credit sharing dominated by the FV automaker, and credit sharing dominated by the NEV automaker. The simultaneous production strategy is the most conducive to both parties’ coexistence in the vehicle market, and the FV or NEV priority production strategy can be adopted to realize the Pareto optimization of their total profit in certain applicable intervals. Credit sharing will greatly change both parties’ applicable intervals and optimal strategy selections, and credit sharing dominated by FV automakers has been proven to effectively improve their social welfare with a low credit price. Interestingly, a high credit price is sometimes more important for the development of NEVs than the NEV cruising range and substitutability under the dual-credit policy. This study also demonstrates the impact of the credit coefficient, credit equilibrium, and NEV substitutability on both parties’ production decisions and credit sharing. Our study has important managerial implications and can be utilized as strategic guidance for FV/NEV automakers to pursue coopetition under the dual-credit policy.