Motivated by the requirements for effectiveness and efficiency, path-speed decomposition-based trajectory planning methods have widely been adopted for autonomous driving applications. While a global route can be pre-computed offline, real-time generation of adaptive local paths remains crucial. Therefore, we present the Frenet Corridor Planner (FCP), an optimization-based local path planning strategy for autonomous driving that ensures smooth and safe navigation around obstacles. Modeling the vehicles as safety-augmented bounding boxes and pedestrians as convex hulls in the Frenet space, our approach defines a drivable corridor by determining the appropriate deviation side for static obstacles. Thereafter, a modified space-domain bicycle kinematics model enables path optimization for smoothness, boundary clearance, and dynamic obstacle risk minimization. The optimized path is then passed to a speed planner to generate the final trajectory. We validate FCP through extensive simulations and real-world hardware experiments, demonstrating its efficiency and effectiveness.