A car is clearly something you will have a hard time to live without in Uzès.
If you land in Paris CDG airport then the simplest option is to take a TGV (high speed train) from the station which is inside the airport to either Avignon TGV, Nimes Pont du Gard, or Nîmes Centre. It takes about 45 minutes from either of those (Nimes Centre is slightly closer). I’m not familiar with the car rental facilities at either, though.
As usual with plane-to-train connections it’s always a bit difficult to get the right timing, as in the best case you could be on the platform well less than an hour after scheduled arrival, or well over two hours (or more if there are significant issues), depending on a variety of factors like your seat on the plane, the terminal and gate, how long the queue at passport control is, and so on. Either take quite some margin and be ready to wait, or book a ticket which is flexible up to the last minute, but in that case, check in advance for your possible alternatives, service patterns are quite irregular.
- going to Paris proper and take a train from Gare de Lyon. More options there, but depending on the day and time it can be a hassle, whether by RER regional train (crowded and delayed) or by taxi (traffic jams). At other times it can be a breeze, so it really depends.
- taking a train to Lyon (airport or Lyon Part-Dieu), as there may be more trains (especially from Gare de Lyon), but then you have a quite bit more road to Uzès (over 2h30).
- flying directly into Lyon or possibly Montpellier, but as far as I am aware, that will necessarily involve a connection somewhere.