Travel from Nice to Boston

First of all you should book your ticket to Switzerland roundtrip but open jaw one ticket for example
Boston to Zurich
Nice to Boston

It is unclear. Did you book a flight from Boston to Switzerland already one way?

Next summer United begins non-stop service from Newark/Nice. So it's a possible connection to Boston on your return leg.

Yes, a multi-city ticket will probably be best for you. Use a flight-search website like Google Flights. Don't try to guess which airline or transfer point to use. Let a website lay out all the options for you so you can choose the best combination of fare and schedule.

If you already have your ticket to Switzerland and only need a one way ticket to Boston then you are a bit more limited in the carriers you can choose for economical fares. I don't think you can fly non-stop from Nice to the US so you will need to get to Paris or some other major city. One option is train to Paris. Another is EasyJet or Ryan air or similar to either Paris or London and from there get a one way to Boston. From London some good airlines to check for one way fares to Boston are Norwegian, IcelandAir and Aer Lingus. Norwegian is nonstop while the other two will have layovers (but usually they are short and painless). Just make sure you leave plenty of time between flights as they will be booked on separate airlines so if the first one is delayed and you miss the second one you are out a ticket. I would probably plan to spend the night but if you found a flight from Nice to London that got there early in the day and a flight to Boston leaving late afternoon that would probably be OK. Depends on how risk adverse you are. Also be aware that London has several airports and can take hours to get from one to another.

I don't think you can fly non-stop from Nice to the US

Next Summer United begins non-stop service between Newark/Nice

I fly BA (Britishairways) from Boston. I would fly Boston to Switzerland, and then Nice to Boston. Changing flights at terminal 5 @ Heathrow. If you watch the routes for a month or two you will see how the price changes, and then buy at a point you are comfortable with the fare.

Delta has direct flights to JFK from Nice from April to October.

As noted, you can do an open jaw ticket from the US and sometimes even get one intra-Europe leg for free. Your return trip can route through a US location (Newark/United, La Compagnie, JFK/Delta) or via one of the European hubs. Nice is the second most serviced airport after the Paris airports in France, thus you can find low cost connections via any portal city, depending on your airline of choice. You might find the connections through Lisbon, London, Brussels, Zurich, Munich and Paris to be the most convenient. TAP via Lisbon and Norwegian (with EasyJet via London) often have the lowest pricing to the east coast.

Any thoughts on best way to get there without spending a fortune and
without too many lay overs? Any feedback would be appreciated!

If this is a one-way ticket to BOS, you will indeed spend a fortune. Why not consider an open-jaw trans-Atlantic routing as others have mentioned; you will undoubtedly save money instead of paying a one-way fare to BOS.