Abou Zeid was a senior figure in al-Qaeda in the Islamic Maghreb (AQIM).
Earlier, French newspaper Le Monde said DNA samples had made it possible to formally identify Abou Zeid.
French troops and a coalition of African forces have been fighting against Islamist militants in Mali since January, the BBC reports.
The Chadian army claimed earlier in March it had killed Abou Zeid and fellow militant Mokhtar Belmokhtar during fighting in February.
"The president of the French Republic confirms with certainty the death of Abdelhamid Abou Zeid after an offensive by the French army in the Adrar des Ifoghas (mountains) in the North of Mali, at the end of February," the Elysee presidential palace said.
The statement said the death of "one of the main leaders of AQIM marks an important stage in the fight against terrorism in the Sahel (region)".
The fate of Mokhtar Belmokhtar has yet to be confirmed.
Islamist rebels seized the vast north of Mali a year ago after a military coup in the capital Bamako.
France intervened militarily in January amid fears that the militants were preparing to advance on Bamako. It currently has about 4000 troops in Mali.