Your entry into the Schengen area is going to be through Switzerland. There are no immigration checks between Switzerland and France anyway so you won't even see any French passport checks. You may possibly see a couple of customs officials as you cross into the French sector, but I doubt they would be interested in passports.
There should be no problem you passing through Swiss immigration with your long-term visa. Unless it's specifically endorsed, it's valid in the whole of the Schengen zone. The immigration officials (Swiss) may ask a couple of questions, but even that's unlikely.
On a practical note, there's no public transportation from the French sector, so you either need someone to collect you or be picking up a rental car.