Bobbity said:
Maylay. Imagine that we're speaking french, and that it's spelled like this: mêlée. The accents change the way in which it's pronounced, so that we say maylay, as opposed to mehlee.
Accents do change the pronunciation, but not always and not necessarily in the way you think. The first accent is a circumflex, and does not change pronunciation (except in Belgian French, maybe). So, essentially, the first accent is useless as a pronunciation guide in mêlée. Therefore, it should be pronounced as a typical French 'me' (which sounds similar to the 'me' in 'meringue'). The second accent is an acute accent, and does change pronunciation to a sound similar to an English 'lay' (not exactly the same, of course - just an approximation).
There are plenty of French words in the English language that have been changed pronunciation and even spelling-wise. Let's not forget that England was ruled by a French-speaking monarchy for a few centuries after William the Conqueror, which added an enormous amount of words to the language. This partially accounts for why we have so many synonyms in English - 'hide', for example, comes from the original Anglo-Saxon dialect, whereas 'conceal' has French origins. So in truth, how you pronounce 'melee' doesn't really matter. Even though we all find pronunciations different from own a bit annoying.
... I need a hobby...