According to the French daily Le Figaro, which said it had seen a secret intelligence memo and talked to well-placed officials, air drops are designed to help rebel fighters encircle Tripoli and encourage a popular revolt in the city itself.
"If the rebels can get to the outskirts of Tripoli, the capital will take the chance to rise against Kadhafi," said an official quoted in the Wednesday report.
"The regime's mercenaries are no longer getting paid and are scarcely getting fed. There's a severe fuel shortage, the population has had enough."
French officials could not immediately confirm or deny the report to AFP.
According to Le Figaro the French arms shipments are dropped from planes in the Djebel Nafusa region, where Berber tribes have risen to join the revolt against Kadhafi's rule and seized several provincial towns.
The crates hold assault rifles, machine guns and rocket-propelled grenades, it said, and also European-made Milan anti-tank missiles, a powerful addition to the rebel arsenal that can destroy a tank or a bunker.
France has taken a leading role in organising international support for the uprising against Gaddafi's four-decade old rule, and French and British jets are spearheading a NATO-led air campaign targeting his forces.
Rebel forces are based in Benghazi in the east of the country, and hold a besieged enclave supplied by sea in the western coastal town of Misrata, but have been unable to mount a convincing advance on the capital.