Bruni-Sarkozy left a Paris clinic on Sunday with her daughter and bodyguards, after giving birth on Wednesday.
President Nicolas Sarkozy said he and his wife felt a "very profound happiness" over the birth of their first child together. He has three sons from his two previous marriages. She has one son from a previous relationship.
Sarkozy is expected to seek a second term in elections in six months.
When the first lady gave birth, Sarkozy was in Frankfurt for an emergency meeting with German Chancellor Angela Merkel, trying to solve the deepening European debt crisis.
Sarkozy is in Brussels all day Sunday for a summit of European Union leaders.