A Total spokesman said "yellow vest" protesters -- so-called because of the high-visibility jackets they wear and which must be carried in all vehicles in France -- were obstructing access to 11 fuel depots.
As a result of the unrest, some 75 fuel stations out of the company's 2,200-strong network across the country were empty because they could not receive supplies, the spokesman added.
Protesters have been blocking roads across France, impeding access to fuel depots, shopping malls and some airports. On Saturday, rioters transformed upscale Paris neighbourhoods into battle zones.
In the Morbihan area of Brittany in western France, authorities were considering restricting the volumes that motorists could buy to prevent more fuel stations running out of petrol and diesel, a local official said.