Autonomous navigation for Unmanned Aerial Vehicles faces key challenges from limited onboard computational resources, which restrict deployed deep neural networks to shallow architectures incapable of handling complex environments. Offloading tasks to remote edge servers introduces high latency, creating an inherent trade-off in system design. To address these limitations, we propose CoDrone - the first cloud-edge-end collaborative computing framework integrating foundation models into autonomous UAV cruising scenarios - effectively leveraging foundation models to enhance performance of resource-constrained unmanned aerial vehicle platforms. To reduce onboard computation and data transmission overhead, CoDrone employs grayscale imagery for the navigation model. When enhanced environmental perception is required, CoDrone leverages the edge-assisted foundation model Depth Anything V2 for depth estimation and introduces a novel one-dimensional occupancy grid-based navigation method - enabling fine-grained scene understanding while advancing efficiency and representational simplicity of autonomous navigation. A key component of CoDrone is a Deep Reinforcement Learning-based neural scheduler that seamlessly integrates depth estimation with autonomous navigation decisions, enabling real-time adaptation to dynamic environments. Furthermore, the framework introduces a UAV-specific vision language interaction module incorporating domain-tailored low-level flight primitives to enable effective interaction between the cloud foundation model and the UAV. The introduction of VLM enhances open-set reasoning capabilities in complex unseen scenarios. Experimental results show CoDrone outperforms baseline methods under varying flight speeds and network conditions, achieving a 40% increase in average flight distance and a 5% improvement in average Quality of Navigation.