... in France last year, for example, I saw signs for "Parking". which is apparently the French word for parking.

There has been a change, then. The last time I was in France - over 40 years ago - the word "Stationnement" as used to proclaim a parking place.
Mind you, the French referred to their car as "une voiture" rather than "un auto", in those days.

"Tout ça change ..." etc.