2
You don't say when you are going from paris to Bayonne, but I just checked at random for the end of February to Bordeaux and got a one-way TGV fare of 25 euros per person. It takes 3 hours, which is the time you would waste going to the airport in advance, waiting around, then flying a short flight and getting from the airport.You have to learn to book in advance if you know your travel dates. Try either IdTGV website or sncf for regular trains (both normal and TCV).
You can also get a direct train to Bayonne, but it's probably longer than going through Bordeaux because it won't be a high-speed line.
4
There are five direct daytime TGVs from Paris to Bayonne. The trip takes around five hours. There is also a direct night train (saves you the cost of a night in a hotel and gives you more daylight hours for sightseeing. See the timetables at www.bahn.de. Tickets can be booked up to 90 days in advance at www.sncf.com. PREM'S (discount) tickets for the TGV can be as low as 25 EUR. PREM'S on the night train can be as low as 50 EUR for a bunk in a six-person couchette and 60 EUR for a bunk in a four-person couchette.
