Sarkozy thanked his supporters Sunday and said he did his best to win a second term, despite widespread anger at his handling of the economy.
He said "I take responsibility ... for the defeat."
A Hollande victory could change how Europe tackles its debt crisis -- with more stimulus and less austerity.
Polling agency projections predict that Socialist Hollande will win the elections. Partial official results also show Hollande in the lead.
Hollande would be France's first Socialist president since Francois Mitterrand, leader from 1981-1995.