Remote sensing semantic segmentation requires models that can jointly capture fine spatial details and high-level semantic context across complex scenes. While classical encoder-decoder architectures such as U-Net remain strong baselines, they often struggle to fully exploit global semantics and structured feature interactions. In this work, we propose HQF-Net, a hybrid quantum-classical multi-scale fusion network for remote sensing image segmentation. HQF-Net integrates multi-scale semantic guidance from a frozen DINOv3 ViT-L/16 backbone with a customized U-Net architecture through a Deformable Multiscale Cross-Attention Fusion (DMCAF) module. To enhance feature refinement, the framework further introduces quantum-enhanced skip connections (QSkip) and a Quantum bottleneck with Mixture-of-Experts (QMoE), which combines complementary local, global, and directional quantum circuits within an adaptive routing mechanism. Experiments on three remote sensing benchmarks show consistent improvements with the proposed design. HQF-Net achieves 0.8568 mIoU and 96.87% overall accuracy on LandCover.ai, 71.82% mIoU on OpenEarthMap, and 55.28% mIoU with 99.37% overall accuracy on SeasoNet. An architectural ablation study further confirms the contribution of each major component. These results show that structured hybrid quantum-classical feature processing is a promising direction for improving remote sensing semantic segmentation under near-term quantum constraints.