According to the French minister des Transports Clément Beaune things are getting better all the time: Pénurie de carburants: " 10% des stations service sont encore en difficulté " this Monday. Some regions are better off than others. In Burgundy (the Nièvre) I tried my luck yesterday evening, no success. Several other fuel stations HS (hors service).
Got fuel (gazol) for two vehicles last week in Soane-et-Loire. Intermarche at Autun and one out in the cuddyside near Saulieu C d'Or/Nièvre boarder - the latter, mega expensive but needed a trickle to get back.
Total Garage on the main road to Mayenne - closed. Intermarche Lassay Les Chateaux - no one at the pumps (there is always someone filling up) OH thought oh well I'll go see and to his surprise filled up with petrol. Guess folks must have thought no vehicles in the station so no petrol to be had.
With this hand, I will lift your sorrows. Your cup will never be empty, for I will be your wine. With this candle, I will light your way into darkness. With this ring, I ask you to be mine.........The Corpse Bride
As I pointed out earlier https://mon-essence.fr has up-to-date reports of places with fuel and prices
There are also Android and Apple apps versions on that page if you are out and about