Accurate short-term electricity load forecasting is essential for efficient grid operation, especially under increasing variability due to renewable integration, electrification, and behavioral shifts. This paper proposes a novel modular hybrid forecasting framework that integrates Fourier series decomposition, Seasonal ARIMA (SARIMA), and a CNN-LSTM residual learning model. The model explicitly captures multi-scale seasonalities (daily, weekly, yearly) using Fourier basis functions, models linear temporal dependencies via SARIMA, and learns nonlinear residual dynamics influenced by weather and calendar variables through a deep learning CNN-LSTM architecture. The proposed model is validated on real-world hourly electricity and weather data from the Korean power grid and compared against several benchmarks, including SARIMA, LSTM, and SARIMAX-LSTM models. Experimental results demonstrate superior performance across all metrics, particularly in peak periods and holiday scenarios. The architecture offers modularity, interpretability, and robustness, making it well-suited for deployment in operational forecasting environments.