Depends on the time of year. I've walked this in early spring and late autumn. If in summer then probably not a lot, assuming you will not be camping, but when I walked I needed gear for every kind of weather, and that is what I got. In early spring and late autumn I had cold, rain and wind, in late spring and early autumn a few very hot days.
It is a few years ago now and I have changed what I take on Camino. Looking at my old photos I see I had a gore tex rain jacket, zip off long quick dry trousers, gloves, a hat, and the ASIC runners (and obviously sock). I recall some very wet days and having to stuff newspaper inside my shoes overnight, but I was much better off than my husband who wore leather shoes that took ages to dry. I also remember I had thermal undies, and a lightweight quick dry technical long sleeve shirt. I took a sleeping bag (much heavier than the down quilt and silk liner I use now).
These days I probably would swop the thermals and shirt for long sleeve merino t shirts and leggings, a Maccabi skirt instead of the trousers, and maybe a down jacket or vest. I'd also use a long poncho or
Altus. Goes over everything and easier to strip off layers. Sandals and waterproof socks.
There are some tricky descents between Le Puy and Conques, going into Monistrol particularly. Looking at Google maps I can see what looks like a road alternative from Pratclau I'd consider.
PS - you probably know, but in rural France food is often hard to come by at the right time. Many of the villages no longer have shops or cafes, the locals drive to larger centres. I had Demi-pension whenever it was offered by the gites (and nice to eat communally). You have to notify the gite before arrival so they can ensure supplies. Otherwise never miss an opportunity to visit a bakery!