Sarkozy has three children from his two previous marriages, while Bruni has a son from a former relationship.
French first lady Carla Bruni was believed to be close to giving birth to her first child with husband President Nicolas Sarkozy on Wednesday, in what would be the first baby to be born to a French presidential couple in office.
Sarkozy arrived on Wednesday afternoon at the La Muette clinic in Paris, where Bruni was admitted earlier in the day, and left half an hour later.
He is expected to fly to Frankfurt on Wednesday for a meeting with German Chancellor Angela Merkel and other euro zone policy chiefs for a meeting on the euro zone debt crisis.
Le Figaro quoted a medical source on its website saying the Italian-born Bruni was in labour, and that the baby was a girl.
Neither the Elysee palace nor the clinic would comment.
France has been on tenterhooks for weeks over the impending birth, with dozens of false alerts circulating in recent days that the baby had been born.
The birth of a baby may give Sarkozy's image a welcome boost just over six months before a presidential election he risks losing to Socialist Francois Hollande.
The birth also comes in one of the most crucial weeks of Sarkozy's four-year presidency as he battles to hammer out a plan with Germany to stem the euro zone's debt crisis ahead of a self-imposed deadline on Sunday.
The publicity around Sarkozy and Bruni having a baby is a novelty for France, where the head of state's private life is usually kept private.
Many in France found Sarkozy's high-speed courtship of Bruni, a singer-songwriter and former model, distasteful coming so quickly after his divorce from second wife, Cecilia.
His image in the weeks and months ahead will be key as he tries to woo back an electorate tired of economic gloom and disillusioned with a leadership manner many see as impulsive and brash, despite his leadership on international issues such as the crisis in Libya.
Sarkozy has three children from his two previous marriages, while Bruni has a son from a former relationship.
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