Wildfires are escalating globally, posing significant challenges to ecosystems and communities. Fire Weather Index (FWI) metrics quantify fire danger conditions. While short-range forecasts provide immediate guidance, extending predictions to 4 weeks could enhance proactive fire management. However, physically-based numerical forecast skill deteriorates beyond ten days. We introduce a deep learning framework that extends deterministic FWI predictions to 31 days by combining data-driven pattern recognition with physically-informed meteorological forecasts. Our model generates more accurate daily 1° resolution FWI predictions. Model training follows a two-phase scheme: pretraining on 16-year reanalysis data to learn global fire-weather dynamics, then fine-tuning on operational forecasts. Compared to numerical baselines, our model reduces global RMSE by ~13% in week 1, maintaining ~6% improvement through day 31, with greatest improvements in grassland and closed forest ecosystems.