This paper studies the influence of free riding on enterprise product pricing and carbon emissions reduction investment, as well as the contract design to achieve supply chain coordination under the carbon trading mechanism. First, we discuss the situation where carbon emissions reduction investment affects the product price and income. It demonstrates that the optimal investment of the upstream manufacturer increases with the degree of the free riding of the downstream manufacturer. The upstream manufacturer can improve their carbon reduction investment and the whole supply chain achieves Pareto improvement when the investment cost sharing contract is introduced. Nevertheless, under the cost-sharing contract the optimal investment of the decentralized supply chain is still lower than that of the centralized supply chain, and only in some particular cases can the two types of supply chain achieve equal total profits. Then, we preliminarily explore the situation where the product price and income is influenced by carbon emissions reduction investment. The consequences indicate that the optimal investment of the upstream manufacturers in this situation is less than the former one’s, and the transfer payment mechanism is able to improve the level of the supply chain overall carbon emissions-reduction. Moreover, compared to the former situation, the effects of free riding of the downstream manufacturer are even more serious. The conclusions can provide some intellectual support for manufacturing enterprises to make reasonable emissions reduction strategies and coordinate the supply chain existing in free riding.