We build and evaluate a probabilistic model designed for forecasting the distribution of the daily mean wind speed at the seasonal timescale in France. On such long-term timescales, the variability of the surface wind speed is strongly influenced by the atmosphere large-scale situation. Our aim is to predict the daily mean wind speed distribution at a specific location using the information on the atmosphere large-scale situation, summarized by an index. To this end, we estimate, over 20 years of daily data, the conditional probability density function of the wind speed given the index. We next use the ECMWF seasonal forecast ensemble to predict the atmosphere large-scale situation and the index at the seasonal timescale. We show that the model is sharper than the climatology at the monthly horizon, even if it displays a strong loss of precision after 15 days. Using a statistical postprocessing method to recalibrate the ensemble forecast leads to further improvement of our probabilistic forecast, which then remains sharper than the climatology at the seasonal horizon.