Islam Times reports from AFP: Libyan state television said late on Saturday that the French warplane went down in the Njela district of the Libyan capital Tripoli.
However, the French military swiftly denied the report.
Foreign forces launched airstrikes against Libya after officials of a number countries meeting in Paris on Saturday ordered a large-scale military intervention into the country in order to end the assaults on civilians launched by Libyan ruler Muammar Gaddafi's forces.
Representatives of the United States, Britain, France, the United Arab Emirates, and Qatar attended the meeting.
There have been reports that French warplanes have begun firing on Libyan government troops in the eastern city of Benghazi, which is the stronghold of anti-government forces.
The French intervention came after forces loyal to the 68-year-old Libyan ruler began closing in on revolutionaries in eastern Libya, despite a ceasefire declared by Gaddafi on Friday.
In addition, US and British forces fired a barrage of at least 110 Tomahawk cruise missiles at Libya targeting Gaddafi's air defenses on Saturday. The missiles reportedly struck pro-government forces.
Speaking to reporters in Brazil, US President Barack Obama said Washington is united with its international partners on the need to take action.
"Our consensus was strong and our resolve is clear. The people of Libya must be protected, and in the absence of an immediate end to the violence against civilians, our coalition is prepared to act and act with urgency," he said.
Libyan anti-government forces, inspired by revolutions that toppled authoritarian rulers in neighboring Tunisia and Egypt, are fighting to unseat Gaddafi after suffering under his despotic rule for over 41 years.