The le Puy route traverses some of the least populated areas of France. Nasbinals is in the center of a kind of dead zone for rail traffic due to its location in the Massif Central. If you backtrack eastwards to Aumont Aubrac, using the services of la Malle Postale, you can catch a train south toward Marseilles. Then you'll have to take a circuitous route to Saint Jean. Similarly, you could use la Malle Postale to get to Figeac on the west side of the Massif Central and train it back to Bordeaux before heading south to Bayonne. Another option which I have read about is to use la Malle Postale to get to Conques and then catch a bus which occasionally may run southwest to Rodez. All of these options involve 9+ hours of transit time.
I would suggest taking an alternate route through France to get to Saint Jean. The Camino Baztan, for example. Or walk from Navarrenx on the le Puy route. Either of these alternatives will give you a taste of Basque country and of walking in France.
I love the le Puy route and highly recommend it. But the difficulty of walking to Nasbinals and then trying to get to Saint Jean is going to be painful, time-wise. I have had excellent, though somewhat dated, experience with la Malle Postale as far as responding to emails in English. You might query them as well.
Transport of luggage and people on many hiking trails
www.lamallepostale.com
Bon chemin. Good luck.
Tom