If you're talking to one person whom you know well (i.e. someone you can address as tu instead of vous): "Qu'est-ce que tu aimes comme musique ?" If you're addressing several people, or someone you...
A person who likes music is properly called 'un audiophile' in French. The term mostly fits people fond of classical music. For other types of music, you may use 'amateur de (+ music style)'. Ex: je...