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.
NATO's war in Afghanistan formally ended on Sunday, when the International Security Assistance Force (ISAF) was replaced by the US-led follow-up mission "Resolute Support".
France, which withdrew all its combat troops from the country two years ago, lost 89 soldiers and saw 700 injured in the war since 2001.
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, who face a major challenge as the international military presence declines.
"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.
"Today, they are evacuating their invading forces from Afghanistan while they are bitterly defeated by the just and pious Afghan resistance," the group said.
"The real solution of the ongoing Afghan crisis is in the complete and unconditional withdrawal of all foreign forces from this country. The presence of foreign occupiers is main cause of instability and chaos."
The Taliban, who ruled Afghanistan from 1996 to 2001, have waged a resilient insurgency against NATO and Afghan forces, with violence now at record levels nationwide.
The United Nations said civilian casualties hit a new high this year with about 10,000 non-combatants killed or wounded -- 75 percent of them by the Taliban.
Insurgents launched high-profile strikes in the capital during the closing weeks of the ISAF era, targeting foreign guest houses, diplomatic convoys, the French cultural centre and Afghan army buses.
The end of NATO's combat mission brought "the longest war in American history... to a responsible conclusion", US President Barack Obama said.
Afghan officials and senior US officers have been pushing Obama to extend US involvement.
US troop numbers are set to halve within 12 months and fall to almost nothing in two years.
President Ashraf Ghani hopes to bring peace to Afghanistan after decades of conflict, saying he is open to talks with any insurgent group.
Since 2001 billions of dollars of aid have been spent in Afghanistan on new schools, hospitals, roads and promoting women's rights. But corruption has been endemic and progress limited, even in the cities.
This year's presidential election, which was meant to be the keystone legacy of the development effort, was marred by fraud and a prolonged standoff between the two poll rivals that fanned further unrest.
At Kabul airport, French soldiers handed a flag to their Turkish successors at an event attended by Afghan officers who will eventually take over the facility.
A memorial in the shape of the Eiffel Tower commemorating the French war dead was also unveiled.
Afghan security forces will hold celebrations on Thursday marking the complete transfer of responsibility from NATO.