From Switzerland to French Riviera

Get a price from the airlines for a multi-city ticket, then you'll have a base-line.

You can fly from Nice to many European cities and connect to US. Paris is one of them, of course.

travel from Switzerland (what city) to French Riviera.

You are starting from wherever you are staying in Switzerland.
And where are you going in the French Riviera? Nice?
The question should really be, "what is the best and practical way to travel from XXX in Switzerland to YYY in the French Riviera".

The answer could be train or fly, depending on where XXX and YYY are.
You can look up train options on the SBB website: https://www.sbb.ch/en/
You just enter XXX and YYY, and your date and time.

Ther are flights from Zürich (Swiss airlines), Geneva (Swiss and Easyjet) and Basel (Easyjet) to Nice. Which is best depends on where you are in Switzerland (XXX?).

The options for flying from the French Riviera are Nice or Marseille airports. Which one is best depends on your final destinatiion in the USA.
List of destinations from Nice airport: https://en.wikipedia.org/wiki/Nice_C%C3%B4te_d'Azur_Airport#Passenger
List for Marseille airport: https://en.wikipedia.org/wiki/Marseille_Provence_Airport#Passenger
Doubling back to a Swiss airport is probably not a good idea.

A flight to Nice is probably the best idea if you are starting from Luzern, the Berner Oberland, Montreux, and anywhere to the north and west of these places.
If you are starting from southern Switzerland however, including Zermatt, Lugano, St Moritz, then train to Milan and connecting train to Nice sounds best, even though Milan to Nice alone is 5 hours on the train.