Well, it was mostly in Italy and the custom sort of spread into France and even England. Commedia dell'arte is also called comΓ©die italienne because it's just 'Italian comedy' and Pierrot is the French version of the name Pedrolino (though I do not think there are the same characters).
Basically, the actors might not even be Italians (performing in France). But commedia dell'arte is Italian and spread to have a French variant.