You've gotten some good advice.
The best train timetable site is www.bahn.de. Click on the flag drop-down menu for English. After you get summary timetables for Amboise-Arles, click on the arrow to the left of each departure time to see the connecting points.
For train travel in France, booking well in advance (up to 3 months allowed) on www.tgv-europe.com will get you the best fares. (Exception: cheap regional trains for which the fare is always the same.) To keep the site in English and to avoid being bumped to the Rail Europe site which doesn't offer discount fares, choose Great Britain as both your country of residence and the country in which you will retrieve your tickets. If you get a Prem's fare, you print the tickets yourself. For any other fare you can pick up your tickets at any SNCF station or boutique (ticket shop) in France, even though you originally chose Great Britain.
No, it is not convenient to get to Beauvais. You have to take a shuttle bus from central Paris and you must leave Paris three hours before your flight's scheduled departure time. It will be much faster to take the train from Paris to Arles than to take the bus to Beauvais, fly to Marseille, and take the train to Arles.
Just as a matter of clarification, Ryanair and other airlines like it are budget airlines, not charter airlines.