Ours just stands for United States Ship, like unto French Ship.
UK vessels are “Her Majesty’s Ship”, I think.
HMS = Her(his)Majesties ship and USS = United States Ship.
The point is that the French do not use such prefixes. Other NATO nations use the appellation FS (French Ship) in order to distinguish them, but the French themselves do not use the prefix. If the French were to use such a thing, they wouldn’t have it in English. It would be something like Bateau de Francais (BDF).