Thanks for all your advices.

Looks like the .357 cartridge would be fun to shoot from a carbine.

OTOH, the .357 cartridge is classified as a "4ème catégorie", here in France, meaning you need a special permit to buy it (same for handguns using it).
Right now I have that authorization, but sometimes I feel it's a PITA to ask for such agrement every 3 years, not being sure the law won't change next year, forbiding such guns' possession.

In that respect (+ cost/availability/weight/versatility), a long gun in .22LR is certainly less of a hassle (no special permit needed) and is also a (technically) good option.