Le Pen was appearing on a current affairs discussion programme on Sunday when she was asked about the president and his wife's latest addition.
"I'm very happy for them," she said. "However, I would have preferred the little girl to have a French name rather than an Italian one."
"I think that when you're president of the French republic, it would give a strong signal to give your child a French name. That's just my patriotic side and I think that lots of French people think the same way as me."
Carla Bruni-Sarkozy left the private clinic in Paris' 16th arrondissement on Sunday afternoon with her new daughter in her arms.
President Sarkozy was able to find enough gaps in his busy schedule over the weekend to visit his daughter. The president has been involved in crisis talks over the future of the euro in Berlin and then Brussels.
German chancellor Angela Merkel and British prime minister David Cameron both came bearing gifts for the new parents to the summit in Brussels at the weekend.
Merkel offered the president a teddy bear while Cameron gave a pink baby blanket woven in his constituency of Witney in Oxfordshire.