The baby – born in the privare La Muette maternity clinic in Paris – is the first baby born to a French presidential couple in office.
It is Mr Sarkozy‘s fourth child – he has three sons from two previous marriages – and Ms Bruni’s second, after her son Aurelien, 10.
Mr Sarkozy was seen on Wednesday afternoon leaving the clinic where his wife gave birth, before heading to Frankfurt for a meeting with German Chancellor Angela Merkel to prepare a eurozone summit to be held on Sunday in Brussels.