The French say the operation is a demonstration of force
More than 1,100 troops have launched a major operation in Afghanistan's eastern Uzbin Valley.
The force includes 800 French legionnaires, together with US and Afghan soldiers.
Ten French soldiers were killed in the area in August 2008 when they were ambushed by Taliban fighters.
A further 21 French troops were wounded, in one of the heaviest tolls suffered by the Nato-led International Security Assistance Force (Isaf).
The operation is aimed at "reaffirming the sovereignty of Afghan security forces in the north of the Uzbin Valley", Col Benoit Durieux of the French Foreign Legion told the AFP news agency.
The French have codenamed the offensive Septentrion. It follows weeks of negotiations with local villagers.
'Demonstration of force'
Last year's ambush was in the area of Sarobi, some 50km (30 miles) east of Kabul.
At the time it was seen as a warning that insurgents were closing in on the Afghan capital, and was thought to be the heaviest loss of life suffered by the French military since 58 paratroopers were killed in Beirut in 1983.
A French military spokesman said Thursday's operation was a "demonstration of force... meant to assure the local population of our presence".
The aim was to plant an Afghan flag in a strategic village in the Uzbin valley.
After several hours' progress, they came under rocket-propelled grenade and heavy machine-gun fire from the insurgents, officials said.
The French responded with shell fire, backed up by French and US air support.
Five US troops were injured - three seriously - and evacuated by helicopter to Bagram air base.
The battle continued for around 90 minutes. A French spokesman said at least one Taliban fighter was killed and three injured.