I think you're confusing English pronunciation of French with French pronunciation...big difference actually. An English speaker will never perfectly replicate French speech so all you can do is get as close as possible. In French René has a growly gutteral throat sound at the beginning that's impossible to illustrate or replicate in English (okay, it's possible, but difficult and I have little faith in most English speakers making the effort) you can hear it from a French native but we all stick to the more universal R sound.
The accent aigu and extra e simply serves in French to double emphasise the syllable and sound. Aimé is Eh-MEH (sounds a lot like 'Emmy'), Aimée is eh-MEY; René is re-NEH, Renée is re-NEY. All that makes perfect sense to a French speaker but an English speaker is going 'what's the difference'? And that's because the vowels of French are rather more subtle than those of English. So how to get around that? Well, they know Renée as re-NAY so working backwards, re-NAY actually has the open mouth end stance of re-NEH so we drop that one completely. Esmé/Esmée is from the same root as Aimé/Aimée so maybe we'll have better luck there. Aimée as a form of Amy everyone gets and most would illustrate that ay-MEE (I'd like to see it eh-MEE but hey, if French was universal we wouldn't be talking now ;o) so how to explain Aimé? Go back to Renée for eh-MAY.
Now, I'd love to pop up some audio files to save myself the trouble of trying to 'translate' from French to English to American because inevitably my memory of American accents is going to fail me and like a Chinese whisper game what comes out on the other end is not at all what I had in mind when I write. I'm sure we'd all love an audio-file sharing system - it's so much easier to hear than to explain. But I'm a realist and I know it's not going to be perfect French no matter how much thought I put into it or how much effort the end user puts into it, just an approximation...hopefully a good one.
The accent aigu is like the E in an open syllable - it sounds like the beginning of 'eight'. I'd personally illustrate that 'eh' but I see lots of people render it 'ay' as in 'ate' so I'll go along with what they already understand it to be rather than be a total pedant and control freak ;o)
So see Esmé isn't an exception at all but then again, none of them are really -ay in French.
Esmé is accepted as a female form because it was traditionally used for both genders once introduced into English, mostly because of the sweet meaning. The development of Edmé helped that along. Even in France, Esmé far eclipses Esmée in popularity and for girls Esma trumps them both. This obscurity helps it be accepted while René is still a much larger presence in French male naming. I wouldn't imagine that there's no female Aimé (I recently saw a female Owen in the birth announcements online) but again, it's such a rare name these days that it probably would be mere curiousity in France and wouldn't even raise eyebrows in English. C'est la vie.
Hope that makes it clearer - I still have this bloody eye patch on so it takes me forever to check that I'm typing what I mean to type! LOL