Il lui manque une case.
eel lwee mahk ewn KAHZ. Click below to hear this pronounced!
He has a screw loose.
Une case is a compartment of some sort: a pigeonhole, a cubbyhole, or even a square on a game board, such as one of the streets in Monopoly or the red and black squares of chess or checkers.
So what does that have to do with the state of this person’s mind?
Since we don’t entirely understand (or even understand at all) exactly how the mind works, we may imagine a Rube Goldberg-like contraption grinding its gears inside our skulls. Hence the screw loose metaphor in English.
But what if our minds are really an old-fashioned mail sorter in a 19th-century post office? Row after row of little wooden pigeonholes in which to file our knowledge, from how to tie shoelaces to Great-Aunt Bess’s middle name, from the best chocolate cookie recipe in the world to the right thing to say when someone says bonjour?
Il lui manque une case is one way to describe that state of affairs: He’s missing a cubbyhole, so he has nowhere to file certain pieces of information. He is eccentric, or slightly unpredictable, or just a little strange around the edges.
The construction il lui manque warrants a brief grammatical observation: il does not mean he here. Il represents it: that is, the current situation, much like It is raining. Lui can mean either to him or to her, so this sentence can actually refer to a man or a woman–either one. So, in the worst possible English, you are saying: It is lacking to him/her a cubby (is missing a cubby). That’s the situation with this person, and you can’t fix it!
Or, if that construction seems like too much trouble, you could always say: Il/Elle a une case vide: He/She has an empty cubby (ell lah ewn kahz VEED).
Note that having a screw loose and losing one’s marbles do not carry the same connotation in English. The first refers to eccentricity, and the second to dementia. Not the same thing at all. The first may be charming, the second is heartbreaking.