Existing cross-border e-commerce (CBEC) logistics supply chain risk assessment often adopts deterministic mathematical model methods, ignoring the uncertainty and fuzziness of data, resulting in inaccurate results and difficulty in adapting to the changing market. To this end, this paper uses fuzzy logic to construct a risk assessment model to solve these problems. By identifying systemic risks in CBEC logistics, risk factors are comprehensively identified and classified, and a comprehensive evaluation indicator system is constructed. Using fuzzy logic methods, a risk assessment framework is built. To enhance the reliability of the evaluation and ensure the consistency and integrity of the data, the entropy weight method is used to determine the weight of each indicator. A fuzzy logic model is established, and a four-layer evaluation model is established for logistics process, environment, information flow and customs clearance risks using membership functions to effectively deal with uncertainty. The fuzzy reasoning rule base is optimized to improve the solution efficiency and accuracy and flexibly adapts to complex supply chain environments. Fuzzy subsets of input variables are defined, and the control rule base is improved. The centroid method is used to defuzzify to ensure the clarity of the model results. The research results show that the average risk identification accuracy of the CBEC logistics supply chain risk assessment model based on fuzzy logic is 94.16%; the average mean square error (MSE) of risk assessment is 0.025; the average response time and sensitivity are 0.691 s and 97.30%, respectively; and the average stability reaches 0.944. The results show that the CBEC logistics risk assessment model based on fuzzy logic can more precisely support enterprise risk management and enhance its competitiveness in the changing international trade environment.