The government says 1,500 of the country's 12,000 petrol stations had run dry over the weekend.
Hundreds of motorists were caught in long queues across France as protesters blockaded the country's oil refineries and fuel depots in opposition to the government's labour reforms.
The action by the General Confederation of Labour (CGT) and Workers' Force (FO) unions was the latest in three months of strikes against a draft law that has set the Socialist government against some of its traditional supporters and sometimes descended into violence.
French oil and gas company Total, which operates five of the eight refineries in France, has started the process of shutting down three, at Normandy, Donges and Feyzin, while its Grandpuits refinery was running at minimum output.
Rival Exxon Mobil said the strike has not affected output at its two refineries, but striking workers had blockaded the oil terminal at Fos-sur-Mer in Southern France.
Oil sector workers in the CGT, which is France's biggest trade union, and at the third biggest FO, said on Monday they planned to intensify the action until the government withdraws a labour reform law, because they say it will hurt workers.
"It is clear that the dissatisfaction with the law is unwavering," the unions said in a statement.
As part of efforts to force the government to withdraw the bill, the union launched a strike at the Fos-Lavera oil terminals on Monday.
Pascal Galéoté, CGT Secretary General at Marseille port said, "No ship is operating at the installations."
The government said 1,500 of the country's 12,000 petrol stations had run dry at the weekend, but did not have up-to-date figures for how many had no fuel Monday.
CGT official Eric Sellini said activists had blockaded 189 fuel depots for several days, though police had since cleared protesters from some of them.
He was unable to say how many were still blocked.
To add to the disruption, tailbacks were building up at those stations still open, slowing traffic on the surrounding roads.
In the cities of Nantes, Rennes and Brest in the northwest, motorists were waiting up to an hour to get to the pumps.
In the southeast at Fos-sur-Mer, near the Mediterranean port of Marseille, about 500 union activists blocked roads leading to a fuel depot with burning tyres.
Another road to the nearby refinery was also blocked.
And in Donges, near Nantes on the northwest coast, union activists used wooden pallets and burning tyres to block access to a fuel depot there.
But France's Socialist government has made it clear it will stand by the controversial labour reforms.
Speaking during a visit to Israel on Sunday, Prime Minister Manuel Valls condemned the blockade of the fuel depots and said the authorities would keep working to lift them.
"I'm asking everyone to face up to reality, not to put the country's economy in difficulty and to respect the users."
Union calls for a Paris strike during Euro 2016.
But the labour unions at the Paris subway company also announced an open-ended strike that would start a week before the opening of the Euro 2016 football tournament in France.
The call for stoppages from June 2 onwards was made by the CGT labour union, and would affect millions of fans and foreigners who are expected to attend the Euro 2016, involving 24 national teams, that runs from June 10 to July 10.
The CGT said that the strike on Paris's metro subway network was being called over pay demands as well as the labour reform, which has sparked waves of street protests since it was hatched more than two months ago.
Metro strikes in Paris usually cause some disruption without paralysing the whole network.