The couple have named the baby Raphael – the same moniker chosen by Charlotte Casiraghi and Gad Elmaleh for their son, who was born in December.
CLICK ON PHOTOS TO ENLARGE
Melissa announced the happy news on her Twitter account. "WELCOME TO THE WORLD! OUR BEAUTIFUL SON Raphaël Blanc just born at the American Hospital of Paris. THERE ARE NO WORDS TO DESCRIBE THE LOVE," she wrote.
The Hunted actress and her millionaire beau have been together for almost two years after being spotted together at a BAFTA afterparty in 2012.
Jean-David is the founder of the French cinema information gatherer-provider AlloCiné.
Former Home and Away star Melissa has previously spoken of her desire to become a mum after meeting her Mr Right.
''I am going to be a mother, absolutely obvious no matter how, when, what. I really am picking the right father for my child. It's very simple.
Melissa tweeted this picture of her baby crib in January as she prepared for the birth
''Words can't describe, sometimes, things that feel so right. I wouldn't want to butcher it by doing that. I had a marriage, and lots of other things, and they were really, really hard. I had to take a break this year. I thank God he dropped this man into my life.''
Melissa ended her marriage to film director Claudio Dabed in 2011. She described him as an "extraordinary man" and said their union was "full of love" but hinted that their relationship stalled over their differing desires to become parents.
Shortly after she and Claudio went their separate ways, she said: "Anyone in their right mind would know what happened.I wanted children, yes, but I still have time. Now I can start from scratch."
The actress also briefly dated Russell Simmons before finding lasting love with Jean-David.