'What size is he?' or 'What size does he take?' are both possible. You could also say 'What is his size?'

Thank you, Den.

Without the context, the question is most likely to refer to something to wear. Using "he" would suggest that a customer is buying for somebody else (3rd person male), and has probably asked about a specific item. The shop assistant would then ask questions like "What is his size?". However, using "his" would apply whether the person is there or not - mother buying for a child, or wife buying for her husband etc., So, the answer is possibly neither! But use "What is his size?" instead.

I see. Thanks a lot, Lee.

A person doesn't have a size. Without context, this sentence makes no sense. Context (surrounding sentences) is needed for this to make sense. For example, my wife and I are shopping for a shirt for me. A clerk is helping us; she knows I am looking for a shirt for me. The clerk may ask my wife, => "What size shirt does he wear?" (specific; good) => "What size does he wear?" (vague - we must know that we are talking about shirts to say this) => "What size is he?" (very vague - we must know we are talking about my shirt/shoe/pant size)