Image compression is essential for applications like satellite imaging, medical diagnostics, and secure communications. Classical methods often struggle to balance compression efficiency and reconstruction quality. Quantum image representations, such as the Novel Enhanced Quantum Representation (NEQR), enable compact encoding using quantum principles like superposition and parallelism. However, quantum-only approaches face scalability and fault tolerance challenges due to Noisy Intermediate-Scale Quantum (NISQ) device limitations. Hybrid quantum-classical methods help mitigate these issues but often lack learning-based optimizations. This paper proposes a Quantum-Classical Hybrid Image Compression (QCHIC) framework that integrates NEQR-based quantum encoding with CNN-based compression. Experimental results demonstrate significant improvements, achieving up to a 196% increase in PSNR, particularly in scenarios where signal fidelity and absolute error reduction are critical, such as medical and satellite imaging. Additionally, the method enhances SSIM by 5%, improving perceptual quality, which is essential for applications where human visual perception plays a key role. These results highlight the effectiveness of the proposed approach in delivering a scalable and high-quality image compression solution for data-intensive applications.