A hailpad network, intended to draw up a large-scale, long-term physical climatology of hailfalls, is being installed in southwestern France, one of the severely hailed regions in the world. The first five years of operation of this network have enabled the organization of a suitable standardization of the data. The classical exponential form is well adapted to represent the mean size distribution of the hailstones sampled at several locations, but we suggest the replacement of the usual concentration parameter of this form the number of zero diameter hailstones by the number of the smallest hailstones really counted on the pads, so as not to amplify, with the regression, a relationship between this parameter and the slope parameter. There is a significant correlation between the concentration parameter and the altitude of the 0 degrees C isotherm level, and a regression enables the determination of a concentration parameter at the 0 degrees C level. By contrast, the correlation between the slope parameter and the altitude of the 0 degrees C level is weak. When these results are compared with Ludlam's model of hailstone melting, they suggest that hail mainly falls within downdrafts. With the limited amount of data presently available, no correlation appears between the distribution parameters and the storm thermodynamics, but the concentration parameter is larger while the slope parameter is smaller in the frontal storms than in the intramass ones, a result explaining why the most severe hailstorms of southwestern France are frontal.