The seismological study of recent seismic crises near Oleron Island confirms the coexistence of an extensional deformation and a transtensive regime in the Atlantic margin of France, which is different from the general western European stress field corresponding to a strike-slip regime. We argue that the switch of the principal stress axes σ1/σ2 in a NW-SE vertical plane is linked with the existence of crustal heterogeneities. Events of magnitude larger than 5 sometimes occur along the Atlantic margin of France, such as the 7 September 1972 (ML = 5.2) earthquake near Oleron island and the 30 September 2002 (ML = 5.7) Hennebont event in Brittany. To test the mechanism of local strain localization, we model the deformation of the hypocentral area of the Hennebont earthquake using a 3D thermo-mechanical finite element code. We conclude that the occurrence of moderate earthquakes located in limited parts of the Hercynian shear zones (as the often reactivated swarms near Oleron) could be due to local reactivation of pre-existing faults. These sporadic seismic ruptures are favoured by stress concentration due to rheological heterogeneities.