The mother is doing well, the friend said.
Sarkozy, 56, was seen earlier leaving the French capital's La Muette clinic, where Bruni gave birth, according to French media.
It is the first child for the couple, who wed in February 2008. Bruni, 43, announced in early September that she was pregnant and vowed to keep the child out of the spotlight.
Sarkozy divorced his wife of more than 11 years before marrying Bruni. He has three children from that marriage.
Bruni, a former supermodel and singer, previously dated singers Eric Clapton and Mick Jagger.
