Train travel from Avignon to Paris

You don't really have a choice. The TGV's from Avignon go to Gare de Lyon on the southeast side of the central city. There are many bus, Metro and RER connections right at the station to get you anywhere in the city, not to mention taxis.

You don't have a choice, all trains from south-east France come into the same station in Paris, "Paris Gare de Lyon".
Just enter Avignon to Paris in your favourite train website (I recommend: https://www.trainline.eu/ ), and it will show you all the trains.
There are two stations in Avignon, "Avignon Centre" and "Avignon TGV". A search for "Avignon" will show trains from both stations.

I just returned from a trip to Europe where I took the train from Paris to Nice. The fast portion was Paris to Avignon. It was very smooth and scenery was really lovely.
The earlier you book your ticket, the better the price. I booked 3 months in advance and paid only about $44 for my whole journey. Yours would be less for the shorter distance. I booked second class and it was quite comfortable. But for the cheapest price, you have to be willing to lock in your particular date and time. There are no changes allowed.
For what it's worth, Gare Lyon is in the Marais and quite close to the the 5th, the Latin Quarter. There are lots of hotels in both areas and are considered pretty central.
Have fun!

I may be wrong (and if I am I'm sure I will be corrected) but Gare de Lyon is not in the Marais district. It is in the 12th arrondisment and on the opposite side of the river from the Latin Quarter. I just want to make sure the OP isn't misled. It is however easy to get from Gare de Lyon to anywhere else in Paris by metro, bus, or taxi, so that is not an issue.

The TGV up the Rhone Valley is a great ride at head-swirling speed and in comfortable seats (even the cheapest). The track is dedicated to the service, with welded rails and hydraulics that keep the cars level on the curves. Some are non-stop; others may make a pause or two but the stations are outside the cities so no slowing down for commuter traffic. In Avignon you will go to the old central station and take a shuttle train to the TGV on the edge of the city. That hop can be included in your ticket and a seat reservation is mandatory.

www.parisbytrain.com will show you photos of Gare de Lyon.
http://www.ratp.fr/en/ratp/c_21879/visiting-paris/ will guide you on mass transit around Paris.
www.seat61.com knows all about trains everywhere.

Thanks for the help so far. Is it better to train from the TGV station in Avignon to Avignon Centre (and in the reverse from Centre to TGV) or do people prefer taxis?

Actually....now that I think of it, the rental car companies are stationed at the TGV stations, am I right? We will be renting and returning a rental car at Avignon. So it probably just makes sense to book travel to and from TGV.

The TGV station in Avignon is a major stop. All of the rental car companies have offices right there at the station.

Actually....now that I think of it, the rental car companies are stationed at the TGV stations, am I right? "

About 100 yards away.

There are a load of car rental buildings right outside the exit and all their cars are parked in the large car park at Avignon TGV, very conveniently just a few seconds walk out of the station doors. All the major rental players have an office there.

Best to get a sat nav on the go when driving out of there as I found the road which follows the river past the city walls a bit confusing at times when trying to get out of Avignon.

Just returned yesterday from Aix-en-Provence to Paris by TGV. This train stops at Avignon, so it's the one you'll be traveling on. I suggest getting 2nd class seats on the upper level. The seats are fine and you get a better view from the upper level. Trip from Aix was 3 hours, so from Avignon it will be slightly less time. This was a last-minute trip so round-trip cost was 150 euros.

We also took the TGV from Avignon to Paris. FYI: since this is not a terminus, the train doesn't stop for very long at Avignon. You need to be ready to find your car and board when it arrives.

As to rental cars, I know that there are plenty of agencies at Avignon TGV. However, last time I was in Avignon center there was just a local car rental company or 2 at that train station.