The first week/ten days (Le Puy to Figeac) will be on the plateau (1200m) and so the nights and mornings will be chilly in October; the afternoons will be favored with warmer sun. Past Moissac, the elevation flattens out until you start picking up the foothills near Navarrenx. From there to Pamplona, you catch the fringes of mountain weather. Of course, the Pyrennees crossing will be the most challenging.
In addition to elevation, one must consider the changeable weather of the shoulder seasons; you'll need to keep an eye on the weather forecast daily. Ask your lodging host for details, if you cannot get the info any other way.
Also many lodgings are only open until All Saints Day (1 Nov); many others will only by open in late Oct if there is an advance reservation. So I think advance reservations will be particularly important.
As to packing, you have the right strategy with layering, for sure. I like the Merino wool base layer. Be ready for wind-driven rain on some days, too.