Meme comes from Greek, not French. If it were a French loanword, you would have been correct. To be specific, it's based on part of a Greek word, but it was coined by a British biologist named Richard Dawkins, so it uses English phonetic conventions.
Loanwords retaining the original spelling is part of why English pronunciation is a mess. Many other languages would have just localised a word like Jalapeno into Halapinyo or something. As things stand, you have to be able to identify a word's origin and know the phonetic conventions of the original language to be able to pronounce half the words in the dictionary properly. At the very least, you need a rudimentary ability to pronounce things in French and Spanish for the great majority of loanwords. Greek and Latin come up frequently as well, but because our Alphabet is Roman, that's not as much of a stretch.