President Nicolas Sarkozy was returning from a meeting in Frankfurt on the euro debt crisis when the child was born around 8 p.m. (1800 GMT) on Wednesday, according to BFM TV.
Europe 1 radio said the birth "went well" for the 43-year-old mother, a singer and former supermodel. She entered the small, private Muette Clinic in late morning, according to the reports.
The presidential palace did not immediately confirm the reports. The presidential entourage reiterated earlier Wednesday that no birth announcement would be forthcoming.
The couple had been coy about the impending birth from the start, with measured doses of information.
The infant would be the first child born to the first lady and the 56-year-old president. The couple married less than four months after Sarkozy took office in May 2007.
The Italian-born first lady has a 10-year-old son from a previous relationship and the president has three sons from two previous marriages -- and is a grandfather since January.
Sarkozy was seen entering the medical facility in western Paris in late afternoon, then leaving about 30 minutes later -- before rushing off to Frankfurt for a meeting on the euro debt crisis. With a scheduled visit Thursday morning to Normandy, Sarkozy was taking a gamble. It was not immediately clear whether he would cancel his visit to Normandy.
The birth ended sometimes breathless speculation about Bruni-Sarkozy's due date. Photographers staked out the clinic since early October, with a security detail limiting their access.
Bruni-Sarkozy has said that she was staying mum about the event because she's superstitious. The couple also decided not to find out the baby's sex in advance.
"You don't have a child for the gallery," Bruni-Sarkozy told French TV network TF1 earlier this month. "I will do everything to protect this child ... I will not show photos of this child, I will never expose this child."