Cradled by her former-supermodel mother and surrounded by bodyguards, the most famous baby in France made her first public appearance today.

Giulia, the four-day-old daughter of Carla Bruni and President Nicolas Sarkozy, appeared on the steps of the Muette Clinic in Paris, where she was born last Wednesday.

Wrapped in a dark blue baby wrap, Guilia was carried down some steps to a waiting limousine with blacked-out windows, and then driven to her multi-millionaire family's town house a few streets away in the city's exclusive 16th arrondissement.

But, despite the kind of celebrity attention which both her mother has grown used to, there was no question of Giulia showing her face to the world.

Mrs Bruni-Sarkozy deliberately covered it up, after announcing last month: "I will never show photos of this child. I will never expose this child."

The French first lady, who has herself chased the limelight almost constantly since first dating English rock legend Mick Jagger as a teenager, added: "I will do everything to protect this infant, and I'll be absolutely rigorous."

As the 43-year-old First Lady and her first daughter left the clinic, there was no sign of Mr Sarkozy, 56, who was away in a meeting of European heads of state.

Last week, he spoke of his "deep joy" at the birth of his fourth child, but made it clear that it would be business as usual as he tried to sort out the Eurozone's growing financial crisis. Of Giulia's birth, Mr Sarkozy said: "Each one of you can also understand that it's an even deeper joy because it is private.' Carla has a 10-year-old son, Aurelien, with a former lover, the philosopher, Rafael Enthoven.

Mr Sarkozy has two sons, 26-year-old Pierre and Jean, 25, from his first marriage to Marie-Dominique Culioli, and a third, 14-year-old Louis, from his second to Cecilia Ciganer-Albéniz.

Pollsters say the birth could give a brief boost to Sarkozy as he grapples with a dismal popularity rating of around 30 per cent before a presidential election next Spring that Socialist challenger Francois Hollande is favourite to win.

Mr Sarkozy, who is 5ft 5 ins, married the then Miss Bruni, 5ft 9 ins, following a whirlwind romance of just 80 days in 2008.

(Read by Emily Cheng. Emily Cheng is a journalist at the China Daily Website.)