About one in 20 petrol stations ran out of fuel entirely and hundreds more faced some shortages, BBC reported citing the government.
Workers blockaded French oil refineries and depots on Sunday in protest over controversial labour reforms.
Prime Minister Manuel Valls said France had sufficient reserves to cope with the blockades.
"We have the situation fully under control. I think that some of the refineries and depots that were blocked are unblocked or will be in the coming hours and days," he said.
Of the 12,000 petrol stations in France, 820 were completely out of fuel on Sunday and another 800 lacked at least one type of fuel, transport minister Alain Vidalies said.
Protesters blocked deliveries from at least half of France's eight refineries in reaction to new labour laws that make it easier for employers to hire and fire staff.
The government pushed through the labour bill on 10 May without a parliamentary vote.
A prolonged strike at French refineries in 2010 resulted in a glut of crude oil in Europe and caused thousands of petrol stations to run out of fuel.