President Nicolas Sarkozy, 56, was returning from a meeting in Frankfurt when the child was born.
Sarkozy has three sons from two previous marriages, while the 43-year-old former supermodel has a 10-year-old son from a previous relationship.
The couple married four months after Sarkozy took office in 2007.
Bruni-Sarkozy has said that she was staying mum about the event because she's superstitious. The couple also decided not to find out the baby's sex in advance.
"You don't have a child for the gallery," Bruni-Sarkozy told French TV network TF1 earlier this month. "I will do everything to protect this child ... I will not show photos of this child, I will never expose this child."
The Associated Press contributed to this report.
