The website most useful for train schedules doesn't show any trains directly from CDG to Bayonne, so you'll have to get to Gare Montparnasse. As others have noted, you'll want to allow lots of time between your landing and the train departure, to cover possible delayed arrival, immigration, baggage claim if any, and getting from the airport to Gare Montparnasse on the other side of Paris.
The cheapest way to make that transfer is a combination of RER "B" rail into the city and Metro within it. Next is Le Bus Direct line 4, from airport to station with an intermediate stop. Most expensive is a taxi costing 55 euros (maybe a bargain if there are more than two of you). Which of these is fastest depends on time of day and traffic. Convenience varies by price. With rail you're taking your bags on and off trains, maybe up and down stairs underground, plus running some risk of theft. With the bus you put them underneath and retrieve them at the station. With taxi they go in the trunk.
If your flight lands early in the morning, you may have time for all this plus the 5-6 hour train ride to Bayonne that same day.
An easier choice, especially if the flight lands in the middle or late part of the day, is to spend that night in Paris and take a morning train. You'll pay for a hotel either way, probably more in Paris than in Bayonne. I'd suggest a place close enough to Gare Montparnasse that you can get there easily for your prepaid morning train. The overnight plan also eliminates worries about getting from airport to station on arrival day. There are many good hotels in all price ranges near Gare Montparnasse, you might try booking.com to see choices on a map, but book directly on the hotel's website if possible.