Can a vaccinated US citizen arriving at CDG hop on a train to Avignon?

A vaccinated U.S. citizen with the CDC card can visit France including any Paris and any other city in France, after a 2week wait after the last vaccination.

Thank you, I was hoping that was the answer, just trying to think of everything in advance. We are flying to CDG, buying our ticket upon arrival and training to Avignon for 2 nights before returning to Paris. Leaving 7/23 and am so looking forward to it. I am 60, traveling with my aunt who is 76.

Is there a Covid restriction for the trains?

Only inasmuch as you must wear a mask on the train.

It's not quite as easy as you make it sound. The Avignon high-speed train departs from Gare de Lyon in central Paris. The airport train you will hop on will be one of the RER regional commuter trains, changing to a second train to get to GdL. There used to be a bus shuttle from the airport to GdL but I don't know the situation post-pandemic.
You might consider another wrinkle: Standard advice has been to buy your high-speed train ticket, which will include a seat reservation, as far in advance as possible, because the advance prices were cheaper. Day-of-travel purchase runs the risk of your preferred train being sold out. And you could face a lengthy line-up at the sales booth. But....there's always a 'but'.....if your plane arrives late, you might miss your reserved train. SNCF used to sell flexible tickets, at a higher price, so you could take a later train, although you still would have to line up to adjust your seat reservation.

Standard advice for train travel almost anywhere is to consult the website Man in Seat 61 so you can be sure of what you face.

Julie, there are high speed trains from CDG to Avignon, Aix and Marseilles. No need to go into Paris.

There used to be a bus shuttle from the airport to GdL but I don't know the situation post-pandemic.

It closed down. Doesn’t exist any more.

https://community.ricksteves.com/travel-forum/france/no-more-bus-direct-old-cars-air-france-in-paris