Car/Train logistics Paris to Provence and back

Yes, the train to Avignon makes the most sense for getting to St Remy from Paris. Tickets may already be on sale because for summer travel on some routes are on sale now. Check trainline.eu. Are your dates in each area set in stone? If they are not, are you open to reordering your itinerary? You are wasting time going back and forth to Paris and having short and proportionally more expensive car rentals.. I would head straight to Avignon and then make my way north and west and then end in Paris. Here is a suggested itinerary if you are open to it (it's got two long driving days but you already have one in your current itinerary so I thought you might be open to two):
Day 1 Arrive at CDG and Train to Avignon and pick up rental car
Day 2, 3 and 4: Provence
Day 5: Drive to Castels
Days 6, 7, 8, and 9: Dordogne
Day 10: Drive to Bayeux
Days 11 and 12: Bayeux
Day 13: Drive to Paris with a stop in Chartes if you are so inclined
Days 14, 15, 16, and 17: Paris
Day 18: Home

"Day 17: Back to Paris. Where to stay convenient to CDG"?

Answer: http://www.accorhotels.com/gb/hotel-1404-ibis-paris-cdg-airport/index.shtml

Day
1. Arrive Paris. TGV to Avignon (4N)
(Pick up hire car during stay in Avignon)
5. Drive via Carcassonne to Castels (3N)
8. Drive to Loire Valley (2N)
10. Drive to Bayeux (2N)
12. Return hire car in Caen. Train to Paris (6N)
(Day trip to Chartres or Giverny during stay in Paris)
18. Depart Paris

I'd stay overnight, if you're coming off a Trans-Atlantic flight.
The train to Bayeux leaves from Gare Saint Lazare, and there are lots of inexpensive chain hotels in the vicinity - TimHotel will suit your budget.
Take the train to Bayeux and pick up a car if you think you need it. You might find it easier to take the train to Giverny, then back to Paris.
You'll need to reserve a car long before getting to Avignon, and can pick it up at the station.
This is an excellent website for all the details you'll need for getting from Point A to Point B by train in France:
http://www.seat61.com/France-trains.htm

Thanks everyone. Yes, our itinerary and lodgings are already set. I just couldn't face heading directly anywhere from Paris after an int'l flight from the west coast, although it would've been smart.

Also, I decided to drive from Paris to Bayeux because I was trying to make the most of time en route to fit in Chartres and Giverny. However, you've given me an idea: Since I haven't booked a Paris hotel for our first night's stay, I think maybe we will just train directly to Bayeux. Maybe we don't need a car really. Or if so, we can rent one there.

Day
1. Arrive Paris. Train to Bayeux (2N)
Pick up hire car in Bayeux.
3. Drive to Loire Valley (2N)
5. Drive to Castels (3N)
8. Drive via Carcassonne to Avignon (4N)
12. Return hire car in Avignon. Train to Paris (6N)
Day trip to Chartres/Giverny from Paris.
18. Depart Paris

"Yes, our itinerary and lodgings are already set."

The OP's itinerary and lodging are already set so there is little point in continuing to offer up alternative itineraries.

@ Chris -- Now that you are considering heading straight to Bayeux, maybe you can see if the lodging that you already have for the nights in Bayeux can just add the third night to your reservation. You probably already know this but just in case, I will mention that you will not be able to take a train directly from CDG to Bayeux. You will have to make your way to Gare St Lazare in Paris to do that and the usual advice is to allow four hours between your flight's ETA and the departure time for the train. What day of the week are you arriving? And are your accommodations in Bayeux within walking distance of the train station? If the answer to the first question is yes or the answer to the second question is no, I suggest that you have your hotel arrange for a taxi to meet you at the train station. Bayeux goes not have, what I would call, a robust fleet of taxis.