Federated learning enables collaborative model training across decentralized clients under privacy constraints. Quantum computing offers potential for alleviating computational and communication burdens in federated learning, yet hybrid classical-quantum federated learning remains susceptible to performance degradation under non-IID data. To address this,we propose FEDCOMPASS, a layered aggregation framework for hybrid classical-quantum federated learning. FEDCOMPASS employs spectral clustering to group clients by class distribution similarity and performs cluster-wise aggregation for classical feature extractors. For quantum parameters, it uses circular mean aggregation combined with adaptive optimization to ensure stable global updates. Experiments on three benchmark datasets show that FEDCOMPASS improves test accuracy by up to 10.22% and enhances convergence stability under non-IID settings, outperforming six strong federated learning baselines.