I think the Camino offers three main options 1) the whole route from Le Puy to Santiago de Compostela, 2) from Le Puy to St John Pied de Port, or 3) from St Jean Pied du Port to Santiago to Santiago de Compostela.
I didn't find Le Puy to be that easy to get to. When I hiked the GR70 from Le Puy I first went to Lyon, (by coach, dreadful) then caught a train (a double-decker, via St. Etienne) to Le Puy. When I hiked the GR65 from Le Puy I first went to Clermont Ferrand, (by train from Dieppe via Paris) then caught a train (two carriages only) to Le Puy. Both of my journeys were rather time-consuming although both routes were very scenic and all of the French trains were really good.
For those who might be thinking of option 3, I suggest two options. To fly into Biarritz then catch a bus to St Jean Pied du Port and then hike on into Spain, (excellent Refuge about 10 miles out on the way to Roncevalles) or for a more demanding and interesting experience, fly into Biarritz (or Bordeaux) catch a train to Hendaye and then hike for 5 days on the GR10 route to St Jean Pied du Port. A really good 'warm-up' experience (and you also see and walk across the tracks of a cog railway) for walking across Spain.