Cross-Domain Sequential Recommendation enhances recommendation systems by integrating user behavior data from different domains, however, it raises critical privacy concerns. To address this challenge while maintaining the quality of the recommendation, we propose the FP2CDSR, a novel federated cross-domain sequential recommendation framework. This privacy-preserving approach leverages federated learning combined with differential privacy mechanisms to generate noise-added user representations while ensuring that user data remains locally processed. The central server coordinates clients, collects, and distributes perturbed user representations to safeguard privacy. Furthermore, we investigate how to effectively restore and utilize semantic information from privacy-preserving data through feature mapping and aggregation strategies. By incorporating self-attention networks and temporal modeling techniques, we optimize cross-domain information integration, refine essential data representations, and enhance recommendation accuracy. Extensive experiments on publicly available datasets demonstrate that FP2CDSR outperforms conventional single-domain and cross-domain recommendation models while ensuring robust privacy protection, validating both its effectiveness and superiority in privacy-preserving cross-domain recommendation scenarios.