Europe 1 radio reported that the child, a girl, was born at the La Muette private clinic in the 16th arrondissement of Paris . The birth was also confirmed by AFP.
Earlier, Nicolas Sarkozy spent half an hour with his wife before leaving for a governmental meeting in Germany .
As the French media reported that the baby was born around 7.30pm local time, it means Mr Sarkozy missed the birth. However, he rejoined his wife and their newborn at 11pm .
Europe 1 radio said the birth “went well” for Bruni-Sarkozy, 43.
No further details were released. It is the first baby to be born to a French presidential couple in office.
According to speculation on Twitter, the baby is said to be named Dahlia or Julia.
Sarkozy has three children from his two previous marriages, while Bruni has a son from a former relationship.