How Does One Pronounce Meme?

I was always puzzled by the term "meme".

I do have trouble, at times, correctly pronouncing fancy words.

I have now seen this, p. 49 here:

The new replicators are called “memes,” a term Dawkins fashioned from a Greek root with an eye towards the French word “meme” (same) and rhyming with the name of the original replicators, gene...

But I have studied French and I do know that that word is pronounced as "m & ms", the candy.  Like the first syllable of "feminine".  The well-know phrase: "plus la change, plus la meme chose".

So why pronounce it like "seam" or "beam"?

^