What else is there to say?
As in most musicals, the dubbing stops when the characters start to sing. They would sometimes dub songs by supporting characters (if there was a separate accompaniment-only track for the song), but the audience would feel cheated if you overdubbed Dean Martin or some equally well-known singer with a separate singing voice.
Also, the fact that the singing wasn't usually dubbed in these films is a data point against the theory that Jerry Lewis was popular in France because of the guy who dubbed his voice. (It sounds weird, but I've heard several people say this in one form or another.) The French, like everyone else in the world, knew what Jerry Lewis sounded like because the dubbed versions used his voice when he sang.
Of course, the whole idea that Jerry Lewis was unusually or freakishly popular in France is a myth that goes all the way back to the early '60s. Given that Lewis was a huge star in American movies until the mid-'60s, it never made much sense to see his French popularity as out of the ordinary; his movies were popular in France, but they were equally if not more popular in America.