French President Nicolas Sarkozy and his wife singer Carla Bruni have announced the name of their new daughter.

The couple welcomed the birth of their first child, a baby girl, on Wednesday in Paris. In a post on her official website, Bruni thanked those who had sent well-wishes and congratulations upon hearing the news of the birth and revealed the child's name for the first time.

"I am deeply touched by the many messages of congratulations that I have received since the birth of our daughter Giulia," she wrote.

"On this happy occasion, my husband joins me in expressing our warmest thanks to all those of you who sent us these tokens of your kindness."

The announcement comes after Sarkozy spoke of his "deep joy" following the baby's birth at a public appearance to the town of Mayenne in France.

"All of you who are parents can understand the very deep joy that Carla and I feel. Each one of you can also understand that it’s an even deeper joy because it is private," he said.

"We have been lucky to have a very happy event take place," he said. "I will just keep to these few brief words to say to you that they are doing very well."

The couple married in February 2009, less than a year after Mr Sarkozy took office, and less than four months after his divorce from second wife Cecilia Ciganer-Albeniz.

The Italian-born first lady has a 10-year-old son from a previous relationship and the president has three sons from his two previous marriages - and has been a grandfather since January.