The jubilee year is for Santiago, and I don't imagine it will cause a huge increase in the numbers walking from Le Puy to Figeac. (Le Puy itself has a different way of working out its jubilee: "the great jubilee which is granted to Our Lady of Le Puy whenever Good Friday falls on 25 March, the Feast of the Annunciation." - from Wikipedia.)
You don't say which month you are planning on walking: one of the busier months for French people walking in this part of France is May, and it can get busy around the times of public holidays. However, I always found a bed, and only once resorted to paying more for a chambre d'hote.
Margaret