Air France has warned that disruption will get worse as a week-long strike by its pilots continues.
It said 60% of its flights were likely to be cancelled on Tuesday as a result of the strike, which began on Monday.
The pilots are protesting against a transfer of jobs by the airline to its low-cost European carrier, Transavia, which is being expanded as part of a new strategic plan.
Air France is urging passengers around the world to change or postpone travel.
It says customers who have booked a flight between 15 September and 22 September can "delay their trip, change their ticket free of charge or claim a refund".
Chief executive Frederic Gagey told France Inter radio that the strike would cost the airline 10m to 15m euros (£8m - £12m) a day.
"[Management is] doing everything to try and find a way out of this situation," he added.
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.