Most common:
* est né(e) (for a male) / est née(e) (for a female) - This is the most common way to say "was born" in French. It literally means "is born".
Formal:
* a vu le jour - This literally means "saw the light of day" and is a more formal way of saying "was born".
Other options:
* est venu au monde - This literally means "came into the world" and is a more poetic way of saying "was born".
* a fait son apparition - This literally means "made its appearance" and is a more literary way of saying "was born".
Examples:
* Il est né en 1980. (He was born in 1980.)
* Elle est née à Paris. (She was born in Paris.)
* Le bébé a vu le jour à l'hôpital. (The baby was born at the hospital.)
The best translation depends on the context and the tone you want to convey.