The first step in probabilistic seismic hazard assessment is the characterization of seismic sources. The fundamental assumption is that the Gutenberg-Richter power law can be applied and is valid at all scales. In this study, we found that the power-law model may not be verified in the southeastern regions of France. Frequency-magnitude distributions are mapped using 2 different magnitude ranges: (1) <3.0--4.4> using only homogeneous instrumental data, (2) <3.5-Mmax(observed)> using instrumental and historical data. b-values estimated on these two magnitude ranges are similar in the Pyrenees and the Rhine Basin. However, they differ significantly in the Southern Alps: the slopes estimated on magnitude range <3.0--4.4> are much steeper (b > 1.4) than the slopes estimated on magnitudes above 3.5 (0.9 < b < 1.1). Until a clear identification of the underlying processes is made, a conservative option (i.e., lowest b-values) should be considered for probabilistic estimation of hazard in the eastern part of France.