The transfer is an important stage in France's withdrawal from the war-torn country, which new President Francois Hollande has accelerated by ordering the return of troops by the end of 2012, a year earlier than previously planned.
NATO's International Security Assistance Force (ISAF) is due to pull out the vast majority of its 130,000 forces by the end of 2014.
Kapisa, an extremely unstable province where French troops have suffered numerous deadly attacks from the Taliban, lies to the northeast of Kabul close to the border with Pakistan's lawless and insurgent-infested tribal areas.
In 2011, 24 French soldiers were killed in Afghanistan, all in Kapisa.
A ceremony in the provincial capital Mahmood-e-Raqi in the presence of French and Afghan military and officials, marked the handover of the province, which was announced by President Hamid Karzai in May.