We would like to explore the Burgundy region for 2 days. We will be in Nice(avec car) and will end up in Paris. Should we drive to Beaune and back to Nice mid-trip, or take a train to Beaune and then a train to Paris for the end of our journey?
You can pick up your car in one city and drop in another. Rental deals may be better with three days, rather than two. Autoeurope usually only arranges rentals for a minimum of three days.
You could rent your car in Beaune and then drive to Paris to drop it at one of the airports and bus or train in.
With only two days you don't have much time to get to and from Burgundy. The train is faster. But, it is nice to have wheels once there.
So I'd go with your second option, but rent either a car or bicycles in Beaune. Take the train to Paris to fly home.
If you really like long drives you could drive to Beaune and/or Paris, certainly not all the way back to Nice.