Unless there is a visible relationship with an already existing feminine French word, foreign words adopted in French are generally masculine and that’s the case with un mème.

Beware that not everyone is already familiar with that word in French, especially as it collides with même.

See also French equivalent of the English “internet meme”?

I’m quoting Richard Dawkins, who created the term :

Le vocable « même » semble lui-même constituer un bon mème.

(Le Gène égoïste [The Selfish Gene, OUP, 1976], Odile Jacob, 1996, chap. XII : « Les mèmes, nouveaux réplicateurs », note 2).