I have no idea what the "correct original" version would be. I only have this site to go on (
http://cafe.rapidus.net/jhuriaux/femmese.html if you are interested) and the name is listed as Emmélise there. I believe the point of the accent is the change the pronunciation. It very well could be wrong in the original French but correct in Quebecois, I have no idea of the linguistic rules of the two variations, but couldn't it be possible that they are slightly different from the original French?
For me personally the point of keeping the accent would be to signify the middle syllable being pronunced closer the -ay sound than the more typical for English -eh.
I'm not bothered about Emme not standing apart. Emmélise is plenty different enough, if (hypothetical) Emme was bothered by the commonness of her nn it's only a nn- she can easily drop it in favour of her full name. NN's are not set in stone :)
Thanks for your input.
Aussie au pair in Switzerland to my French-Italian girls
Sass (Feb '08), Boof (Jan '10) & Pixie (Dec '11)
http://www.behindthename.com/pnl/56287