Melee is a French-derived word meaning the same thing we use it for in english. The french spelling is mêlée. It's a conjugation from the verb mêler, which means to mix, blend, or combine.
The accent (the little slashes above the e's) change the pronunciation in french. If an E has no accent over it, you pronounce it almost like you would in english. However, if it has an accent over it the E is always pronounced like "ay" as in May-lay.
mêlée ---------> melee
When the word was converted to English, it lost the accents because those don't exist in the English language. However, words taken from another language are generally expected to be pronounced somewhat like they were in the mother language. Therefore.... may-lay is the most Frenchish way I've heard it pronounced, although the correct way is possibly closer to meh-lay.
*the accent is only over the second-from-last E. I'm certain the closest to the correct way to say it would be something like meh-lay, however I'm no expert in French. I only took it for a few years
http://www.wordreference.com/fren/mêlée
