In France you have to carry them in the Allps in winter. And they check!
Not so, Charlie. This November marks the introduction of a law requiring chains (carried ) or snow-tyres (fitted) in 48 dépts from Nov 01 to Mar 31. In the past , when the weather was bad ( Saturdays only when the tourists arrived ), the gendarmes would only allow cars with chains up the hill into the resorts. I often wondered what the thousands of unequipped did, because local outlets only stocked a couple of hundred sets.
You're obviously a multi-tasker ! Pools on one forum and snow-chains here
I use 195/65 x 15 in winter, preferring to go for a slightly skinnier tyre, and 215/55 x 16 other times.
Best place to get wheels would be a scrapper. Don't forget wheels are not necessarily unique to a car and you should investigate which other ( possibly more common/cheaper ) makes use the desired size/hole arrangement.
I don't know what chains you have, but by their very fitting method, chains generally cover a WIDE range of sizes.
Many people fit winter-tyres on steel-wheels, but I guess you'll be consulting the wife on that possibility.