Car rental in Bordeaux

I can't answer your question specifically, but we just did a pick up and drop off in two other locations in France, using Enterprise Car Rental. They have reasonable fees for dropping off in a different location. You may want to check with them.

Are we nuts to think we can fit 4 people and 4 bags into 1 car??

If you select the right size car, it will not be a problem.

Just make your car rental reservation on AutoEurope and use Carcassonne as the pick up spot and Bordeaux St Jean (the train station) as your drop off spot. That will answer the question of which rental car company will work for your plans,

BJT,
Re your car size..Last year .we were four adults, each with a carry-on size bag and a backpack (or equivalent) and rented an intermediate sized car. It was the perfect size. At one point, two of our party rented the same size car and had to (twice) fit five people and all their luggage in for a three hour drive. Two were kids, but not little kids (9 and 12). They managed, but I wouldn't want to do much driving in that size car with more than four people. What the rental information may say is that there is room for four people and four or five bags, but that is often stretching it a bit.
Back in the day (the seventies) a Deux Chevaux was listed as a four passenger convertible! (I think the roof rolled back like a sardine can before there were pop-tops!)
My point is to be sure of the size because the luggage takes up a lot of room.
Bon voyage!
P.S. We picked up and dropped off at the Bordeaux train station. A little funky finding the Avis site, but GPS helped a lot. There was a good deal of road construction going on nearby, with some roads closed. Open hours at Bordeaux are pretty good. I don't know about open hours in Carcassone. Do go through Autoeurope to see all your options.

Thanks everyone for the great suggestions!

Carefully check the opening hours of rental agencies in Carcassonne.
It is often closed on Sunday and sometimes also on Saturday and also.... during meal times.

If you are going from Carcassonne to Sarlat and want to enjoy the road here is a much more scenic route than the motorway via Toulouse:

https://maps.app.goo.gl/8yRzTPZsqKSG9BSx6

That's 1 hour more driving time without counting possible stops in the "Most Beautiful Villages of France" in:

Puycelsi

https://www.la-toscane-occitane.com/en/the-fortified-village-of-puycelsi

and Bruniquel

https://www.la-toscane-occitane.com/en/sheets/bruniquel-cite-medievale-bruniquel

(I sometimes take this route, the last time was yesterday)

Thank you for the sightseeing suggestions between Carcassonne and Sarlet!!! Extremely helpful