A dictionary on the interweb suggests that it is pronounced mey.ley
Which is the easiest way to type it in a post without using a whole lot of special characters.
I'm not much scratch on phonetics but I'm fairly certain that makes it sound very much like May Lay, although it is a french word and the french have a wicked sense of humor when it suits them. The dictionary also suggested that the word could be related to 'medley', possibly because they are both borrowed wholesale from french and are only different by a slight movement of the tongue. I'd argue a whole letter can represent a world of difference, but I said I wasn't much scratch with phonetics. Or Etymology neither.
You, OP, asked how I say it. That would be me.lay. Only because I'm childish and it makes me giggle. I play some pen and paper rpgs, and they give you a surprising surplus of opportunity to utter the word mêlée and, in the heat of the moment, I occasionally hear myself shortening it to meh.lay.
That's what SageSays