Strictly speaking, Vichy was not the capital of unoccupied France during WWII, since France continued to exist de jure (if not de facto) as a whole from 1940-44 and its capital was still Paris (some ministers even officially kept their main offices there).
Vichy was "only" the seat of the French government, and French administration (police, departmental civil servants, etc.) continued to exist on both sides of the demarkation line.
This is in many ways the same as saying Berlin was the capital of West Germany, although most government and public service centers and other state institutions were in Bonn.
There are many countries that have no official capital (there isn't a single law stating that Paris is the capital of France, for example), but most of those countries at least acknowledge that they have a de facto capital. Switzerland is pretty unique in being quite strenuous about the fact that it has no capital city. Bern is simply where most government institutions are located.
Villa in Italian does not mean "Country" home. It's just a home. It's a term often used to identify larger than average homes, or more luxurious ones, while small ones may be called "Villetta". Villas can be anywhere including big cities, not only country.
Why? It's a 20-question quiz. There are 44 countries in Europe. How much over-representation of the UK would be adequate? Plus I'm quite sure if there was a question on here about a US state the whining would be deafening.
Vichy was "only" the seat of the French government, and French administration (police, departmental civil servants, etc.) continued to exist on both sides of the demarkation line.
Could you not even stretch to something like 'US state named for Elizabeth I'?