Bruni-Sarkozy, 43, has an 11-year-old son from a previous relationship, while Sarkozy has three sons, aged 26, 25 and 14, from two previous marriages. Bruni-Sarkozy checked in to the Clinique de la Muette in western Pariswhere an entire floor was cleared to ensure her privacy and security.
A crowd of photographers and television crews had been waiting for more than a week behind barriers 200m away.
Sarkozy visited for 30 minutes about four hours before the birth, then travelled to Germany.
Earlier this week, he told journalists travelling on his private plane that he hoped "Carla doesn't give birth on [Monday]", when he is due to attend the make-or-break eurozone summit in Brussels.
The Elysee Palace said it would not make any comment about the birth. Last month, in one of her few interviews on the subject, Bruni-Sarkozy, said she would never allow any photographs of the child to be published.
"You don't have a child to play to the gallery and my position as the wife of the head of state has made me even more defensive.
"I understand the media interest and I don't see any inconvenience in it for myself or my husband, but when it concerns the children it is impossible."
Some of Sarkozy's supporters have expressed the hope that the "baby dividend" will benefit him in the affections of the French public.
The President's popularity has sunk to new lows in recent weeks. A poll published yesterday suggested that, if the second round of presidential elections was held next weekend instead of in May, he would lose to Socialist candidate, Francois Hollande by a crushing 62 per cent to 38.
- INDEPENDENT
