The handover took place at a ceremony in the provincial capital, Mahmood-e-Ra qi and “lets everyone see that Afghans are taking over their security”, a French official told the AFP news agency.
But it will have little effect on the ground.
French soldiers will continue to train Afghan National Army troops and, after 2,000 are pulled out this year, 1,500 will remain for training and to organise the return of equipment.
The French lost 24 soldiers in 2011, all of them in Kapisa, which is north-east of Kabul near the provinces of Kunar and Nuristan, where insurgents are very active.
France is the fifth-largest contributor to Nato’s International Security Assistance Force (Isaf), which is due to pull its 13,000 troops out by the end of 2014.
Apart from the eurozone debt crisis, the presence of troop in Afghanistan was one of the few foreign policy questions to feature prominently in this year's presidential election, with both leading candidates promising to bring them home but Hollande setting an earlier date than outgoing president Nicolas Sarkozy.
Thousands of Pakistani truck drivers on Wednesday prepared to resume Nato supply convoys across Pakistan after Islamabad agreed to left a seven-month ban following a US apology for a US air raid that killed 24 Pakistani soldiers.