"montre" as a noun is a watch, the object used to keep track of the time.
This is what a French will mean when he'll use the word as a noun. "montre" can also be a conjugation form of the verb "montrer" ("to show").
There are a few other translations, but they're not used at all in common French (in fact when you asked this question I made a research out of curiosity, and I didn't even know that "montre" could be used other ways as a noun, even though I'm French).
Here is what I found if you're still interested :
In the other hand, "watch" has many different translations in French, both as a noun and a verb.