PARIS — Proud papa Nicolas Sarkozy, the first French president to have a baby in office, says he and wife Carla Bruni-Sarkozy feel “a very profound happiness” over the birth of their baby girl — the couple’s first child together.

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

After keeping the nation guessing, the first lady announced the baby’s name on her website: Giulia.

“I’m very touched by the numerous messages of congratulations that are coming in since the birth of our little girl Giulia,” Bruni-Sarkozy wrote.

After being unusually coy about the pregnancy, Sarkozy was ready to brag.

“We are lucky to have been blessed by a new arrival,” Sarkozy told journalists on a visit Thursday 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.”

Privacy was the guiding principle of the baby’s hush-hush birth Wednesday. Police officers posted outside the maternity clinic kept journalists at bay, and it was only Sarkozy’s frequent visits Wednesday that tipped the news media off as to what was going on inside.

The tight control over news of the birth appears to be part of a strategy aimed at portraying Sarkozy as absorbed in resolving the problems gripping France and Europe.