Vehicular Fog Computing (VFC) is a promising paradigm to meet the low-latency and high-bandwidth demands of Intelligent Transportation Systems (ITS). However, dynamic vehicle mobility and diverse trust boundaries introduce critical security challenges. This paper presents a novel Zero-Trust Mobility-Aware Authentication Framework (ZTMAF) for secure communication in VFC networks. The framework employs context-aware authentication with lightweight cryptographic primitives, a decentralized trust evaluation system, and fog node-assisted session validation to combat spoofing, replay, and impersonation attacks. Simulation results on NS-3 and SUMO demonstrate improved authentication latency, reduced computational overhead, and better scalability compared to traditional PKI and blockchain-based models. Our findings suggest that ZTMAF is effective for secure, real-time V2X interactions under adversarial and mobility-variant scenarios.