Federated Learning (FL) enables collaborative model training without sharing raw data, yet practical deployments suffer from severe data heterogeneity and partial client participation, which often lead to unstable convergence and biased global updates. To address these limitations, we propose Class-Coverage Sampling with Entropy-Weighted aggregation (CCS-EW), a lightweight and heuristic client-selection and aggregation framework. CCS selects clients by greedily maximizing per-round class coverage based on their local label histograms, ensuring that selected clients collectively provide a broader class coverage. EW further computes Shannon-entropy–based weights to amplify contributions from clients with more balanced data. Experiments on non-IID CIFAR-10 show that CCS-EW achieves higher accuracy (51.3% vs. 34.8%) and significantly improves client-level fairness and convergence stability. These results demonstrate that CCS-EW is an effective and efficient solution for heterogeneous FL.