If you want to avoid France and Switzerland you need to go a long way East and then cut through Austria 😯
Mate who does delivery driving often goes via Luxembourg (cheap fuel) then Germany to get to Milan but does cross Switzerland.
It is not as though there is NO fuel in France although its getting more tricky, a few days ago we got a full tank of “regular” unleaded but some garages have run out of certain grades and many have a €20-30 limit (although pumps don’t turn off they just get “upset” at cashier – return with gallic shrug 😉 )
I would keep an eye on the news, French government are now involved and understand how important tourism and half term is. I’ll ask Mrs B for an info website. I am confident they will supply major petrol stations, prices may be high though (was about €1.29 up till now)