Well, it was mostly in Italy and the custom sort of spread into France and even England. Commedia dell'arte is also called comédie 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.