How to say the sentence from the title. I know the affirmative version: Il a l'air heureux. But the question remains evasive: Il a quel air? Quel air a-t-il? Sounds a bit rough, cannot explain why.
Avoir l'air is a rather ambiguous expression to use for a question. The question might also be about someone's appearance or intentions, so it's hard to tell what kind of answer you are seeking.
If you are specifically asking about a person's mood, you could ask
Quelle est son humeur?
I think most French people would say: "Il a l'air de quoi?", or more formally: "De quoi a-t-il l'air?".
This could however be interpreted as pertaining more to the physical appearance of the person. A way to ask the question that may be closer to your emaning would be the say: "Il a l'air comment?", although this is not particularly formal.