Very likely they would refer to the EU standards pickworthi mentions above, for the basis of their 250W definition, non?
Laws are written in imprecise natural language, perhaps for the benefit of lawyers who need to feed their families, and I wouldn't bet my life that "moteur auxiliaire électrique" in that context, means only the component that here on endless-sphere we call the "motor." If you swap in your own controller & battery and start feeding that motor 40A, they'll say "no, your controller is part of that auxiliary motor system." Or they won't, who knows. Does anyone here even own a France-legal bicycle, is there a sticker somewhere?
The "arrête de pédaler" part is like the law here in my state, in that it requires the pedals to be operated - but doesn't require any sort of correspondence between pedal input force or cadence. I think that's typical of such laws, if only because the common implementation is split between force ("torque") and cadence and the legislators don't care to get into that. So while it's commonly implemented with one of those two proportional pedal assist systems, it doesn't have to be that fancy, just on / off.