I must say I didn't know what a tumbler was, so I searched for pictures with Google and from what I saw, I'd say "verre droit" is a good translation for a glass tumbler.
If it is a steel tumber, I'd rather call it "un gobelet [en métal]".
The glass tumbler is called a gobelet or verre droit. The metal tumbler is definitely not called a verre droit, however. I think it might be a cylindre - it depends on the context - for example there's a kind of lock that uses tumblers where the term in French is "goupilles".