Check the route and times on the DB website because it is the most complete for trips of this kind:
https://www.bahn.de/p_en/view/index.shtml
I put a random Sunday date into the DB schedule and found this:
There is one high speed train that goes from Avignon TGV station at 13:21, arriving in Tours St. Pierre station at 15:29. The local train to Amboise leaves at 18:10, arriving in Amboise at 18:21.
You can save some time by dropping your car at the Avignon TGV station instead of the Arles station. That way you avoid having to take either a connecting bus or local train.
Other than this, there are routes that connect in Paris. If you choose the Paris route, choose a train that arrives at the Gare de Lyon with a connection at the Gare d'Austerlitz because these are an easily walkable half mile from each other. Otherwise, you have to take a metro across Paris to the Gare Montparnasse to connect.