The French national airline has asked passengers to check their flight status before travelling, as a pilots' strike coinciding with Euro 2016 caused it to cancel some flights.
About a quarter of Air France pilots were on strike but the company said more than 80% of flights went ahead.
Some Paris-Marseille flights were cancelled on Saturday, affecting fans travelling to the England-Russia game.
The strike will continue for three more days.
The pilots' union Spaf (Syndicat des Pilotes d'Air France) is taking action because of planned pay cuts and changes to working conditions.
It is one of many unions taking action; others are striking because they want the government to scrap new labour laws that will make it easier to hire and fire people.
Rubbish will not be collected in Paris until Wednesday, train services have only recently resumed after a nine-day strike, and at the end of last month many petrol stations ran dry when protesters blockaded oil refineries.
In a statement, Air France said 7% of long haul flights, 9% of domestic flights and 27% of medium haul flights were cancelled on Saturday.
The company had said it would prioritise flights to cities that were hosting Euro 2016 tournament matches, but four out of seven Paris-Marseille flights were cancelled on Saturday.
The airline said a higher proportion of Sunday's flights would be affected, and that information about the following days would be published soon.
It offered to allow passengers to postpone their travel by up to a week at no extra cost.
The company's chief executive, Frederic Gagey, has said that the dispute will cost the airline €5m (£3.9m) a day.
In all, seven million people are expected to visit the 10 French cities where matches are taking place.
President Francois Hollande has warned unions against disrupting the tournament.