I think this may be a BE/AE thing.1. What make is your watch? ~It's a Rolex.
2. What brand is your watch? ~It's a Rolex.
"Marque" was used for cars, particularly at the luxury end of the market, but I doubt it has been current for forty years or more, and "make" is a lot more common, in BrE at any rate. I don't recall "marque" being used for anything other than cars.I also found a synonym - 'marque'.
I would only say "What make is your watch?" In BE, referring to the brand seems to be over-concerned with fashion, or the ability to afford a status symbol. (And after all, watches are made by watchmakers.)