Judging by this single picture, I'd say this watch looks basically legit, it's from the very early 1950s (likely from 1950) and maybe a ref. 2577.
As has been said above, you need to have the watch opened to know for sure what you have there. Don't try to open this watch on your own, because you'll cause damage to the case. Ask a good watchmaker to help you and tell you more.