Smart healthcare IoT systems are vulnerable to cyber threats as they deal with sensitive patient information. Problems such as privacy, scalability, and delayed response to threats in distributed healthcare environments challenge centralized security approaches. To mitigate the security challenges of cloud-edge healthcare IoT systems, this paper presents FL-EZTF, a privacy-preserving, Federated Deep Learning and Enhanced Zero Trust Framework. The framework combines federated learning, Enhanced Zero Trust Architecture (E-ZTA), and Secure Access Service Edge (SASE). In this framework, lightweight deep learning models are developed locally at hospitals and various edge nodes without the need to transfer sensitive medical data. In place of raw data, model updates are sent conveniently through a trustaware federated learning process. Simultaneously, E-ZTA performs continuous authentication, micro-segmentation, and access control to rapidly contain threats. The framework is assessed using CIC-IoT-2023, IoT-23, and WESAD datasets. The experimental results show improved accuracy in detection, lower rates of false positives, a significant reduction in the latency of decisions, and enhanced containment as compared to centralized and traditional federated learning.