"He is a cook."
Translation:Il est cuisinier.
Professions don't use articles in French. "Il est cuisinier" is perfectly fine.
Look at Note 1 at the end of the list: http://french.about.com/od/vocabulary/a/professions.htm
I'm a native English speaker, but a word of advice for the future: if you think something doesn't sound right you shouldn't describe it as "caveman-like."