Pilots for Air France have begun a week-long strike.
The carrier will run less than 50% of normal flights, it said.
The pilots are protesting against a transfer of jobs by the airline to a low-cost carrier to keep up with competition.
Air France is urging passengers around the world to change or postpone travel. Last week it said it would transfer much of its European operations to low-cost carrier Transavia.
The same difficult conditions are faced by large airlines across Europe, facing tough rivalry from budget airlines and Gulf state carriers, that are often backed by royal families.
Chief Executive Frederic Gagey told France Inter radio that the strike would cost the airline 10m to 15m euros (£8m – £12m) a day.
The airline said it would consider negotiation on benefits based on seniority for Air France pilots who agree to work for Transavia.
However, it said it would not agree to trade union demands that the contracts of Transavia pilots carry the same terms as those flying under Air France.
Separately, the Vereinigung Cockpit union, which represents Lufthansa’s pilots, says they will cease working from Frankfurt airport for eight hours on Tuesday, preventing departures by Germany’s biggest airline from its busiest airport.
There have been several strikes in the past three weeks by Lufthansa pilots in Munich and pilots at Lufthansa’s Germanwings business.
That strike is over early retirement terms.