Il fait gris.
This literally translates to "it is gray", but it is understood to mean overcast.
Here are some other options:
* Le ciel est couvert. (The sky is covered.)
* Il y a des nuages gris. (There are gray clouds.)
* Le temps est nuageux. (The weather is cloudy.)
The best option will depend on the specific context and nuance you want to convey.