I was going to walk the Podiensis in late March in 2020.
I also found booking was difficult as many places didn't open until Easter. I started planning and booking in October/November 2019 but found that many places didn't reply until January as they were waiting to do their new prices for 2020. I found that I had to adjust my distances to suit where I could find a bed. Of course you could just adlib and walk until you come to a town and poke around or ring around until you find a bed, but the idea of walking to a town through a day of sleet and possibly having to continue to the next town in the fading light of short March days was not at all appealing. Also many gites will open if they have a booking, but would otherwise be closed to the casual drop in walker. They like to be able to prepare the meals knowing how many mouths they are to feed and how many rooms to heat during the off season. I also found that logistically it was impossible to do the Cele variant as I just couldn't find enough accommodation in the low season.
Frustratingly, I had just got the last place booked and my itinerary sorted when that night Australia announced that we were shutting our borders and we couldn't leave or return so I spent the next few days undoing all of my bookings.
My process for booking was to use the Gronze, Miam Miam Dodo and also to use Google Maps and expand the towns on the GR 65 and see what gites, hotels and even BnBs and Air BnBs were available. Some of the most enjoyable nights were at farm homestays.
You may have to use a taxi to skip a section if there is no accommodation to be found, or to go off the path by taxi then return to that spot the next morning if things are really grim. Also, you may need to taxi bypass the Aubrac Plateau if late snow is closing the route.