You can usually get one of "quick, cheap and easy." Sometimes you can manage to get two. Rarely do you get all three...

There are no direct trains and no flights from CDG to Vichy. Trains leave from Gare de Lyon in Paris. The trip takes a little under three hours. Unfortunately there are not a lot of direct trains on this route. Advance purchase PREMs fares would be the least expensive but note that they are non-refundable and cannot be changed once booked. I have not checked but the lowest fares should be less than €20 single, €40 return. You cannot book more than three months ahead but should book as early as possible within that time frame if you want to take advantage of the lowest fares. You can find timetables and book on tgv-europe.com or raileurope.co.uk and should probably check both to see which site will give you the best deal.

The best combination of cheap, quick and easy in terms of getting from CDG to Gare de Lyon would be to take the direct Air France coach from the airport. Be sure to allow ample time to get to your train especially if you opt for the PREMs tickets.

http://videocdn.airfrance.com/cars-airfrance/