There are several factors to consider in your plans. The first is the two-week mid-term school holiday running the last two weeks of October, which will reduce the number of lodgings that are open, meaning that you will need to plan further ahead. The second is the weather, especially at elevation: snow cannot be ruled out on the Massif in early November (although it is unlikely). So you will need to carry gear for cold/wet. The third factor is All Saints Day on Nov 1, after which a large number of lodgings will close, which again means you will need to plan further ahead.
Given that the route from Geneva to Le Puy is nominally 4 weeks, you would be in the higher elevations the later weeks. From Le Puy, you would be moving to lower elevation in the later weeks, and there are good transit connections in Cahors, which is nominally 3 weeks from Le Puy. I would vote to start this trip, this year, from Le Puy.
