Carla Bruni-Sarkozy and baby doing "very well," Nicolas Sarkozy says

French President Nicolas Sarkozy and his wife, Carla Bruni-Sarkozy, await the arrival of G8 member state leaders and their spouses for an evening dinner on May 26, 2011, in Deauville, France.

(CBS/AP) PARIS - Nicolas Sarkozy, the first French president to have a baby while in office, said Thursday he and wife Carla Bruni-Sarkozy feel "a very profound happiness" over the birth of their first child.

Mother and daughter, he added, are doing very well.

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It was the French leader's first official comments about the birth, which took place Wednesday at a maternity clinic in western Paris. He did not give the baby's name, in keeping with the couple's coyness throughout the pregnancy and labor.

"We are lucky to have been blessed by a new arrival," Sarkozy told journalists on a visit to a waste management plant in western France. "All parents can understand the very profound happiness Carla and I feel, and at the same time everyone can understand that this happiness is all the more profound because it is private."

When asked about the baby's name, Sarkozy said he'd "allow the mother the pleasure of telling you herself."

Bruni-Sarkozy confirmed the pregnancy in July. In a rare interview during her pregnancy, Bruni-Sarkozy vowed to keep her baby out of the spotlight and pledged not to release any photos of the infant. She said in another interview that her pregnancy was "unimportant" to the French people.

This is the first child for the couple, who married in 2008. Sarkozy, 56, has three sons from two previous marriages, while Bruni-Sarkozy, 43, has a 10-year-old son from a previous relationship.

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