You're welcome. As long as you don't need to do the full journey in 1 day you have plenty of options. Here are some of them :
Bordeaux on Sunday crossing Paris :
- from your hometown to Lille-Flandres (5 min walk)
- TGV Lille-Europe - Paris-Nord 12:05 - 13:23 (or earlier or later from Lille-Flandres too) 10€
- transfer by RER (not included)
- TGV Paris-Montparnasse - Bordeaux 16:03 - 18:44, 18:24 - 21:44 (10€) or 19:08 - 21:14 20€
Bordeaux on Sunday avoiding Paris :
- from your hometown to Lille using reservation-free ICs
- TGV Lille-Flandres - Bordeaux 17:16 - 22:02 20€
The next day : easy reservation-free TER journey to Hendaye.
Book TGVs within France here (4€ booking fee per order compared to 2€ per person per train on interrail.eu) : https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish
You can also better check availability there. Do not hesitate for questions. Would you have another stop than Bordeaux in mind ? Most of the above TGVs also stop in Poitiers or Angoulême.