Upvote:3
Yes, you will be OK (provided everything else is in order). For this purpose, you can look at the the whole Schengen area as a single country. You can only enter from a non-Schengen country once but you can leave and enter a particular Schengen country as many times as you want as long as you are not leaving the area.
There can always be some random passport check (it seems somewhat common when coming from Italy) but you won't get an entry or exit stamp when traveling between France, Italy and Switzerland. In fact, there probably won't be a police check at all, even if you are flying.