Air France said it cancelled around 20 percent of its flights on Monday as pilots protested against government plans to make strikers give at least two days' notice when they planned to stop work.
At airports such as Toulouse in the southwest, up to half of all flights were cancelled. A spokesman for the airline said further cancellations were possible as the day wore on.
The country's main pilot union, SNPL, said 50 percent of pilots stopped work on the first day of a strike over the government decree, which will last until Thursday night.
This strike is widely backed and will increasingly be so, SNPL spokesman Louis Jobard said.
Transport Minister Thierry Mariani stood firm, saying the government would go all the way with legislation that would allow airlines to plan minimum services rather than finding out of the day of a strike just how many of their staff refused to work.
The right to strike is there, and the right to strike will remain, but passengers will at last have some rights, he told RTL radio.
Air France shares were hit, trading down 3.8 percent at 5.13 euros late in the trading day versus a 0.3 percent decline in the European travel and leisure index
One investment analyst, who asked not to be identified, said the strike was the first test for management since it implemented a restructuring plan. The financial situation could rapidly get complicated if the industrial unrest were to drag on, he said.
(Reporting by Chine Labbe; Writing by Brian Love; Editing by Ben Harding)