|Sarkozy, who was absent when the baby was born, arrived to the maternity clinic in west Paris few hours later [AFP]
Carla Bruni-Sarkozy, the French first lady, has given birth to a baby girl, the first infant born to a sitting president of modern-day France.
Nicolas Sarkozy, the country’s president, who was attending a meeting in Germany on the eurodebt crisis, was absent when the baby was born on Wednesday evening.
He arrived at a private clinic in western Paris at about 11:00 pm local time [21:00 GMT], just over three hours after the birth, the AFP news agency reported.
Sarkozy left the hospital shortly after midnight without talking to the assembled reporters.
Europe 1 radio said the birth "went well" for the 43-year-old mother, a singer and former supermodel.
"For the moment we don't know the little girl's name," a source told AFP.
The girl is the French first couple's first baby since their marriage in 2008, although Bruni has one 10-year-old son from a previous relationship and thrice-married Sarkozy has three children aged 14 to 26.
In an interview pre-recorded for French state television, due to broadcast on Thursday, Bruni-Sarkozy said she had not known the baby's sex: "We've arranged for it to be a big surprise. Obviously, a nice surprise."
Earlier this month, she told French TV network TF1: "You don't have a child for the gallery."
"I will do everything to protect this child... I will not show photos of this child, I will never expose this child."
The Elysee Palace office has said it will not make any official announcement on what it considers a private family matter, but the birth was widely reported in French media outlets.
The 56-year-old centre-right leader is languishing in the opinion polls, far behind newly-crowned Socialist challenger Francois Hollande, and faces a tough battle for re-election in next April's first round vote.
Political scientists told AFP that any "baby bump" in the opinion polls would be short-lived and arrive too late to in itself save Sarkozy from the ignominy of a single-term presidency.
In the run-up to the birth, Bruni-Sarkozy insisted political considerations and timing - including the expectation of a birth in mid financial crisis - had not been taken into account as the family made its plans.
She said any baby's arrival is "a happy carefree moment and that's how it's been since the dawn of time".
"We're in a time of crisis, but if human reproduction was decided by thinking about whether you're going to have a perfect life, we wouldn't be here to talk about it, neither you nor I," she told a journalist.