Carla Bruni gave birth to baby girl at Muette Clinic in Paris.

Carla Bruni, France First Lady has given birth to a baby girl this evening at Muette Clinic in Paris.

According to sources, President Nicolas Sarkozy spent half an hour with his wife Carla Bruni shortly after she delivered their first child together.

Carla Bruni and Nicolas Sarkozy insisted that the happy event should remain a “private matter” and no official announcement will be made by the Elysee Palace.

Carla Bruni, 43, who already has a son from a previous relation, has even claimed that that her second child will never be pictured.

President Nicolas Sarkozy, 56, paid the 30-minute visit to his third wife at the clinic before heading off to a meeting with German Chancellor Angela Merkel in Frankfurt.

On arrival in Germany Nicolas Sarkozy refused to respond to any questions about his fourth child.

Carla Bruni becomes the only serving First Lady in French history to have a baby.

France First Lady was seen arriving at the private Muette Clinic early in the morning.

One member of the private clinic staff confirmed later: “She’s had the baby, it’s a little girl.”

By Wednesday evening, leading French TV stations, including France 24, which is funded by Nicolas Sarkozy’s government, were reporting that “numerous sources” inside the clinic had confirmed the birth.

“Speculation is rife that France’s First Lady may have given birth,” said presenter Francois Picard.

Jeremy Trottin, of BFMTV, another non-stop Paris news channel, said: “There are reports that Ms Bruni-Sarkozy’s gynaecologist has already delivered the baby.”

Le Figaro reported earlier on Wednesday that Carla Bruni had gone into labour.

Police and plain-clothes security agents surrounded the clinic in Paris’ 16th arrondissement, close to Carla Bruni’s town house next to the Bois de Boulogne.

President Nicolas Sarkozy arrived with presidential aids for his visit shortly after 4:00 p.m., local time, and half-an-hour later headed off to Germany looking impassive.

Carla Bruni has a 10-year-old son, Aurelien, with a former lover, the philosopher, Rafael Enthoven.

Nicolas Sarkozy has two sons, 26-year-old Pierre and Jean, 25, from his first marriage to Marie-Dominique Culioli, and a third, 14-year-old Louis, from his second to Cecilia Ciganer-Albeniz.