There were no demonstrators or police at Total's headquarters building, located in the Paris financial district of La Defence, reporters there said.
France has over 12,500 petrol stations and Total supplies half of the country with petrol.
Oil prices were supported near $80 per barrel by the ongoing strikes by French oil workers.
Environment Minister Jean-Louis Borloo told Europe 1 radio France was not at risk of running out of fuel and had around 10 days of stocks. "At this point in time, there is no risk of shortage," he said.
But analysts expect shortages to worsen rapidly as the strike spreads and French families take to the roads for school holidays.
Petroleum industry body UFIP said on Monday there were around 7 days of fuel supply left.
UFIP head Jean-Louis Schilansky told BFM radio on Tuesday the Total strike, which is also due to spread to Exxon's two French refineries on Tuesday, did not threaten to paralyse the country in the short term.
"But it's true that if this situation continues, this tense situation will lead more or less to problems towards the end of next week," Schilansky said.
(Writing by Marie Maitre and Jo Winterbottom; editing by Marcel Michelson)