About 150 French soldiers who had been helping run the military airport handed over responsibility to a Turkish unit which will operate under the new NATO mission.
France, which withdrew all its combat troops from the country two years ago, lost 89 soldiers and saw 700 injured in the war, which began in 2001.
NATO combat operations officially ended on Sunday when the International Security Assistance Force (ISAF) was replaced by the US-led follow-up mission "Resolute Support" which will concentrate on training and support.
During the final weeks of the ISAF era, insurgents launched several high-profile attacks in Kabul, choosing foreign and diplomatic targets including the French cultural centre.
The conflict against the Taliban still rages across Afghanistan, and an estimated 17,000 foreign soldiers will stay on to assist the local police and army.
"The threat is still present, insurgents continue to be active, but what has been accomplished in 13 years is considerable in terms of governance, development, security," said General Gratien Maire, second in command of the French military.
The soldiers could leave with "the satisfaction of a duty well done" he said.
The foreign force next year will consist of the 12,500-strong NATO mission, most of them US troops, and a US counter-terrorism operation outside the NATO remit, though final numbers remain unclear.
The Taliban issued another statement on Wednesday celebrating the end of NATO's combat mission, adding that no peace talks could happen before all foreign troops leave.