Apart from the trains, try looking at the cheap airline companies for cheap flights. They will be reducing their summer coverage at the end of September, but it is still worth checking perhaps going from Biarritz into the UK, or CDG Paris and then back out to Lyon or Geneva, or train to Bordeaux then fly somewhere. Easyjet also fly to Geneva from Toulouse. You could combine the train with a flight. Ryanair or more difficult to work out without looking at the Route Map because they use smaller airports and I don't think they fly to Geneva, but they do fly into Italy - Turin, etc. The search engines with the big travel companies do not add these cheap companies in - presumably because they do not receive any payment or commission. So log onto Easyjet for example, see where they go and what combinations you can work on, ditto with Ryanair. There are other companies as well but as I am English I only use the ones that go back and forth into the UK.
Goodluck, Buen Camino, Bonne Camino. I hear the Le Puy route is lovely so can't wait to give it a try myself. Ange