How to understand rail lines?

Pretty easy. Trains to Avignon go from Gare de Lyon.

There are not many different Paris train stations you can go to; each station serves only particular parts of France or international lines. You rarely have any choice as to the station in Paris you will use. When you explore options, you will use the sncf site and put in Avignon as your departure and Paris (all stations) as your end point and the site will show which train station serves Avignon. I would assume Gare de Lyon.

A bit terminology: A rail line is physical infrastructure, which is usually not that interesting. But from Avignon to Paris you will mainly take LGV Méditerranée, LGV Rhône-Alpes and LGV Sud-Est.

As mentioned, you buy a ticket to Paris (all stations) and you will see which station your train arrives at. If you want to see beforehand, this map can be useful: https://commons.wikimedia.org/wiki/File:Railway_stations_on_departure_from_Paris_map-en.svg

By the way, there are two train stations in Avignon: Avignon Centre and Avignon TGV, about 3 miles south of town.
Most trains to Paris leave from Avignon TGV: to reach it, you can either take a shuttle train from Avignon Centre (not free! so book a ticket from Avignon Centre if you intend to use it), or arrange a cab (won't cost much).

Thanks so much! All really helpful information!

For future reference, the site www.seat61.com can be helpful for almost any train question.

The TGV line from Avignon to Paris is dedicated to those fast train. The station, on the edge of town, has only two platforms, one for TGVs to Paris and the other for Marseille and points east. Your train ticket includes a reserved seat and there should be a diagram on the platform showing access to that car.
A polite reminder that the trains run on the 24-hour clock, so an afternoon departure at 14:00 hours is 2 pm, not 4 pm.
Local, slower trains used to connect through Lyon, on a separate set of tracks, from the old station just outside the Avignon city walls. It is far slower but you might get a better look at the far distant French alps.
Arrival point, as mentioned, is Gare de Lyon. That big and confusing station does offer what must be the greatest train-station restaurant anywhere, Le train bleu.

also look on Youtube for train vloggers who have done that route, they are quite plentiful (the vloggers that is).