Loin des yeux, loin du coeur = Far from eyes, far from heart = Out of sight, out of mind.

Faute d'un point, Martin a perdu son ane = For the lack of one point, Martin lost his donkey = A miss is as good as a mile.

Quand le chat n'est pa la, les souris dansent = When the cat's away, the mice dance = When the cat's away, the mice will play.

Une hirondelle ne fait pas le printemps = One swallow doesn't make a spring = One swallow doesn't make a summer.

Ne vendez pas la peau de l'ours avant de l'avoir tue = Don't sell the bearskin before you've killed the bear = Don't count your chickens before they've hatched.

and, not a maxim, but an idiom which I must mention:

Avoir la langue bien pendue = to have a well-hung tongue = The gift of gab.