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The rapid expansion of multi-cloud ecosystems has intensified the demand for privacy-preserving analytics across untrusted infrastructures. This paper proposes Federated Zero-Trust Analytics (FZTA), a framework that integrates federated learning, zero-trust security, and privacy-enhancing computation to enable secure data collaboration without centralized trust. The design combines continuous identity verification, decentralized policy enforcement, and hybrid cryptography based on homomorphic encryption and differential privacy. Evaluation across three commercial clouds demonstrates that FZTA achieves near baseline model accuracy (within 2% of centralized training) while maintaining (ε<1.2, δ=10−5) differential privacy guarantees and less than 20% computational overhead. The framework resists eavesdropping, replay, and model inversion attacks while meeting compliance standards such as GDPR and HIPAA. Results confirm that strong privacy and federated scalability can coexist under zero-trust conditions, establishing a foundation for secure cross-domain analytics in healthcare, finance, and IoT applications.