Fresh product traceability plays an integral role in ensuring food safety. Recently, many firms have introduced blockchain technology (BCT) for product traceability to guarantee product authenticity and consumer rights. However, introduction of the new technology has also intensified the competition among fresh products. Meanwhile, previous studies on traceability strategies only considered the impact of traceability cost and ignored the issue of increased product competition in blockchain era. Driven by these problems, we build a game-theoretical model to analyze the optimization of traceability schemes for both low-end fresh products (LEFP) and high-end fresh products (HEFP) in a fresh product supply chain (FPSC) in a competitive environment. Moreover, this paper investigates the impact of power structure on traceability schemes and identifies the conditions under which one scheme outperforms the others. We find that the cost per unit of product input has no effect on the traceability decision of the FPSC. Nonetheless, the introduction of BCT increases the number of consumers who choose LEFP and raises the selling price and wholesale price of corresponding products. Finally, from the supply chain perspective, it is best to adopt the same traceability scheme for both products. This study sheds light on the use of BCT in traceability can provide enhanced product authenticity and consumer rights while increasing product competition and demonstrates the significance of traceability schemes in the FPSC.