TGV tickets from Paris to Avignon

You can start at: http://en.voyages-sncf.com/en/?DISTRIBUTED_COUNTRY=GB
Use the ticket collection country as France. Shop for your tickets, prices will vary depending on the departure day and time. Call your credit card co and let them know your are purchasing a rail ticket in France. If you have difficulty with the transaction, use https://www.capitainetrain.com/en.
They sell the tickets at the same price, and the credit card verification process is easier.
There is no discount for round trip, so buy two separate one-way tickets.

If you book early enough to get the cheapest "Prems" fare through SNCF, which go on sale about three months in advance, then you can pay with PayPal and avoid credit card issues. See Rick's French ticket tips. This won't count as a roundtrip if both ends are not at CDG, so book it as separate, one-way tickets.

You depart from Gare de Lyon and can return to CdG. But think very cautiously if you expect to catch a flight the day of return. The basic website is http://en.voyages-sncf.com/en/
If you specify Antarctica to receive tickets you probably will be able to print them out at home, so you can walk straight onto the train. You don't even have to stamp them at the machine on the platform like machine-issued tickets.

The conductor will scan the ticket, maybe but not often asking for your passport or the purchase credit card.
Some travellers prefer the site www.capitainetrain.com including the Man in Seat 61 whose own website is basic training for all train travel www.seat61.com

I am making this trek from Paris to Avignon in May and have done so before. I purchased online at http://www.sncf.com/en/passengers. When making your reservation, choose France as your ticket collection country. You will actually be printing your tickets from home, however. Let your bank know of your online purchase(s) ahead of time or risk getting your card blocked during the process. It happened to me. If you depart from one station but return to another, it will require a separate reservation. Round trip tickets depart and return from the same station.

If renting a car, choose Auto Europe http://www.autoeurope.com as they are a rental firm representing several different rental car companies (Hertz, Europcar, Avis, etc..). You will rent from Auto Europe, but pick up your car from one of these companies, and you will get the best price. They all rent similar vehicles and classes.

I would take the train from Gare de Lyon station and return to the same. I would not count on taking the train from Avignon to Paris on the same day to catch a plane home. That's an awful lot of travel in one day. Although the train will be relatively on time, unforeseen circumstances can happen. And, with the horrible check-in lines at CDG and security delays, do you really want to risk it? Spend a last memorable night in Paris instead.