Is French just the most commonly spoken common language, even in Germany and Czechia?

Not at the slightest. I suppose it's just a marketing thing where french sounding names are supposed to be more appealing or tell something about the food or atmosphere at the hotel. And based on a very quick visit at booking.com I don't see any french sounding hotels at Berlin, so I don't know how many there actually are. I'm sure there's some around like everywhere in the world, but I think majority is something else.

And there's a lot of shared history between countries, so that can mix things up in various ways.