Switzerland is in Schengen now. Makes no difference whether the immigration you go through is Swiss or French. Same procedure as if going through CDG.

Your bags should be checked through from the US to NCE when you travel all legs on "one" ticket. And should be transferred behind the scenes without the need for you to pick it up in GVA. When in doubt, ask your airline about the procedures.

When you arrive at the Swiss sector of GVA, you go through Schengen immigration. When you then transfer to your Gate in the French sector, there will be Customs (technically), but it's more a walk-through with very rare spot controls than any time-consuming activity.
Schengen is only for people, not goods. Which has no importance for your trip, though.

"Schengen is only for people, not goods."

Makes me think of who you are, and what you are trying to smuggle

Thank you rkkwan and Cowboy, I've never used the French Sector of this airport so this is good info.

Dayenu, please stop posting my secrets!! How do you think I finance all of these trips?

P_M

Which airline(s) are you flying to and from GVA, and from where will you be flying to GVA? The answers to those questions will determine which hurdles you need to clear in GVA.

Further relevant question: is your entire xxx-GVA-NCE itinerary on a single ticket?

So many parameters to consider

It is a single ticket. I'm on United from AUS/IAD/GVA then Swiss to NCE.

OK, in that case your luggage will be checked all the way through to NCE, (make sure the check-in agent actually does this!) and UA should be able to issue boarding passes through to NCE.
At GVA, you will still need to pass through:
1) Swiss immigration
2) Swiss customs
3) French customs
4) Security

Basically, just follow the exit signs when you land in GVA. Once you've passed through Swissimmigration, the luggage hall (just keep on going, your luggage won't be on the belt) and Swiss customs, you'll be landside in the arrivals area, turn left, and walk a short distance to the esalators on your left. Take the escalators up one level to the check-in area and turn right; you will see signs for the French sector as you reach the far end of the check-in area, near the Air France ticketing counter. Follow those signs, you will go through French customs and end up in the small French sector landside area. The security check will be right there, and the gates just beyond.

This may sound a bit long and confusing, but can easily be done in 20 minutes from landing as long as the queue at immigration moves quickly. Unless your inbound flight is seriously delayed, you should be absolutely fine. Worst case, Swiss will most probably re-route you via ZRH.

Hope this helps,
Andre

For most vacation travelers, the most useful feature of the France/Switzerland option at GVA (and also Basel, when the latter had more significant service from SR) is the ability to rent a car either from the French side or the Swiss side. If you want to p[ick up the car in Geneva and drop it off somewhere in France, it's almost always a LOT less expensive to rent from the French side.

You can also save by doing it the other way around -- picking the car up in France and dropping off at the French side at GVA. However, you'll need a decent map, as there's a special access road to the French side (côte française) that is not so obvious to find.

Thanks for the detailed info, I appreciate all responses.

Even yours, Dayenu.