The fuel pipeline to Paris's main airports has been shut off amid strikes over government pension reforms.
The company that operates the pipeline told French media that the capital's main airport, Charles de Gaulle, could run out of fuel as early as next week.
There are fears of fuel shortages as all of France's 12 oil refineries have been hit by strikes, and many oil depots remain blockaded.
Unions are opposed to government plans to raise the retirement age.
Trapil, the firm that operates the pipeline to Paris's airports, said supplies had been cut off on Friday.
A company spokesman told AFP news agency: "Orly airport has stocks for 17 days, and Roissy [Charles de Gaulle] for at least the weekend."
The pipeline is supplied by the Total refinery at Grandpuits, in Seine-et-Marne, which is in the process of stopping production because of the strikes.
A spokesman for Aeroports de Paris, the authority that operates both airports, told Reuters news agency it was "not at all worried about stocks" - but did not say how long these would last.
In recent days government officials have tried to play down fears of petrol shortages, insisting that France has enough to see out the industrial action.
However, panic buying has broken out in some areas, putting supplies under greater strain.
Fuel distributors said several hundred filling stations had to close because supplies had run out.
Earlier on Friday, riot police reopened oil depots that had been blockaded in Fos-sur-Mer in the south, Cournon in central France, and Lespinasse and Bassens in the south-west, AFP reports.
But strikers threw up fresh pickets in at least five fuel depots - at Caen and Ouistreham in the north, Le Mans and Vern-sur-Seiche in the north-west, and La Rochelle on the Atlantic coast.
French Junior Transport Minister Dominique Bussereau told reporters: "We cannot afford petrol shortages. One must bear in mind those of us who need transport."
On Thursday, France's petrol distributors urged the government to release emergency fuel stocks, warning that only 10 days' fuel was left.
Demand at petrol pumps has surged by 50% in the past two days.
In the port of Marseille, more than 70 ships carrying crude for refining are stranded as dockers continue their rolling strike.
The protests erupted after centre-right President Nicolas Sarkozy announced plans to raise the minimum retirement age from 60 to 62, and from 65 to 67 for a full state pension.
More than a million people took to the streets in the latest national protest on Tuesday.
France's main unions have since stepped up their action, calling for the fifth in a series of strikes and street protests on 19 October.
"This movement is deeply anchored in the country," CGT union leader Bernard Thibault told LCI television.
"The government is betting on this movement deteriorating, even breaking down. I think we have the means to disappoint them."
France's main lorry drivers' union, CFDT, has called on its members to join Tuesday's strike.
The BBC's Christian Fraser in Paris says another concern for the government will be the growing involvement of the student lobby.
Students, who joined Tuesday's demonstrations in large numbers, held further protests on Friday.
Riot police used tear gas and made 16 arrests as they fought running battles with secondary school students in the central city of Lyon.
More than 300 secondary schools across France - about one in 15 - remain affected by strikes and blockades.