Most places in France think that when you order a Martini you want a glass of vermouth, not a cocktail. And if you give them the ingredients they will say "ah like a vodka martini but with gin?" ...

That's mostly because "Martini" is the prevalent brand of vermouth in central Europe. It's super confusing... https://en.wikipedia.org/wiki/Martini_%26_Rossi

But France is Western Europe, not central. Is it the prevalent brand there too?

>Usually the countries considered to be Central European are Austria, Croatia, the Czech Republic, Germany, Hungary, Poland, Slovakia, Slovenia, Switzerland; in the broader sense Romania and Serbia too, occasionally also Belgium, the Netherlands, and Luxembourg.

I think that Martini was overwhelmingly the most prevalent brand of vermouth the world over. That's certainly the case in the US.

Vermouth is from Italy, which is more Central European than Belgium, the Netherlands, or Luxembourg.

I've never heard people refer to Italy as "central Europe", personally.

Yea. Made that mistake before. Got vermouth with a slice of lemon