It said the move could be part of a new Afghan policy being worked out by President Nicolas Sarkozy and his advisers.
About 1,900 French soldiers are based in relatively calm Kabul and Le Monde said the fresh troops would be deployed outside the Afghan capital.
"Their destination would be zones of potentially fierce fighting, preferably the eastern region of Afghanistan close to the tribal areas of Pakistan," the newspaper said, giving no source for its story.
Early last year, France withdrew 200 special forces soldiers who had been operating under U.S. command in Afghanistan. Le Monde said Paris was now expected to sanction the return of the special forces.
A presidential spokesman declined to confirm or deny the newspaper report. "The president has not made a decision. We are in discussion with our partners, inside NATO but not exclusively," he said.
Washington is heading a campaign for what it calls a fairer sharing of the burden in the fight against Taliban insurgents. Britain, Canada, Poland and others have backed the United States.
Sarkozy said in December that Paris could boost its presence in Afghanistan but the presidential spokesman said earlier this month that no decision had been reached.