Paris to Nice flying

Is your flight to the US on the same booking as your flight from Nice? In that case no problem as it is still the airline's job to get you home.
If your flights are no on the same ticket than this may end up bing a problem. This is one reason why one should not book connecting flights separately.

I normally take the high speed train between Paris and Nice as it's not much different than flights (about 5H:37M). However if you've already booked your flights, I guess you'll have to stick with that.

Should we be concerned about getting to Paris in time for our flight back to US?

If the flights are the same day and NOT a single booking, yes, you should be very concerned.

How much time between the arrival of the one and departure of the other?

You haven't given enough information. Which airline: EasyJet or Air France? Which airports: only CDG or are you changing from Orly to CDG? Your itinerary: all on one ticket or two separate tickets and airlines? How big of a change: five minutes or two hours or a different day?

Bets is correct, not sufficient information. From Nice to Paris, or the opposite, I always fly into ORY as my destination is typically the Left Bank. My door-to-door time is much faster (and usually cheaper) to fly than to take the train.

You have different objectives. Most US departures are early in the day. Either way, fly or train, you need to be in Paris/CDG, the night before your scheduled flight to the US.

Fly into Nice with a connection set up by the airline. Work your way back to Paris on the ground and then fly home, again on the same airline. Using a multi-destination search, the flights will all be part of one itinerary which provides back-up and often costs about the same as a simple round trip.