The victims - a man, a pregnant woman and a child - were travelling in a car that failed to stop at a checkpoint in northern Kapisa province.
The French ambassador has apologised, but President Karzai said no apology could bring back the dead and he called on Nato to protect civilians.
France has a total of 4,000 soldiers serving in Afghanistan.
Earlier this month French President Nicolas Sarkozy announced that the country would withdraw 1,000 of these troops by the end of 2012.
Nato and French military spokesmen said that the car carrying the three people failed to stop at the checkpoint on Wednesday despite repeated warnings .
The French soldiers then fired into the car, killing three civilians.
The issue of civilian casualties caused by international forces has been a source of tension between Nato and President Karzai, says the BBC's Bilal Sarwary in Kabul.
Nato is currently conducting investigations into such incidents, including the killing of a female doctor and the wounding of five children.