Cross-market recommendation (CMR) aims to enhance recommendation performance across multiple markets. Due to its inherent characteristics, i.e., data isolation, non-overlapping users, and market heterogeneity, CMR introduces unique challenges and fundamentally differs from cross-domain recommendation (CDR). Existing CMR approaches largely inherit CDR by adopting the one-to-one transfer paradigm, where a model is pretrained on a source market and then fine-tuned on a target market. However, such a paradigm suffers from CH1. source degradation, where the source market sacrifices its own performance for the target markets, and CH2. negative transfer, where market heterogeneity leads to suboptimal performance in target markets. To address these challenges, we propose FeCoSR, a novel federated collaboration framework for cross-market sequential recommendation. Specifically, to tackle CH1, we introduce a many-to-many collaboration paradigm that enables all markets to jointly participate in and benefit from training. It consists of a federated pretraining stage for capturing shared behavior-level patterns, followed by local fine-tuning for market-specific item-level preferences. For CH2, we theoretically and empirically show that vanilla Cross-Entropy (CE) exacerbates market heterogeneity, undermining federated optimization. To address this, we propose a Semantic Soft Cross-Entropy (S^2CE) that leverages shared semantic information to facilitate collaborative behavioral learning across markets. Then, we design a market-specific adaptation module during fine-tuning to capture local item preferences. Extensive experiments on the real-world datasets demonstrate the advantages of FeCoSR over other methods.