Air France pilots have called off a strike that has lasted for two weeks and cost the airline hundreds of millions of euros.
Pilots' union SNPL and the airline have yet to reach an agreement over a dispute about the carrier's plans to expand its budget subsidiary Transavia.
However, a union spokesman said it was ending the strike so negotiations could "continue in a calmer climate".
The loss-making airline wants to cut costs to compete with budget carriers.
Although the strike is now over, the two parties failed to resolve their differences during weekend talks.
Air France said it "deeply regrets that, despite lengthy negotiations since the beginning of the conflict (including 15 hours yesterday)... the balanced and reasonable protocol to end the conflict proposed by management has not been signed by the unions".
On Friday night, the airline rejected an offer by SNPL to end the strike if an independent mediator was appointed.
The government, which owns a 16% stake in the airline and has pressed hard for an end to the strike, also rejected the offer.
As a result, Air France announced late on Saturday that it would be operating less than half of its scheduled flights on Sunday.
It has now said flights will "gradually return to normal" from Tuesday - those flights cancelled on Sunday and Monday would remain so.
The airline and union will continue talks over employment contracts.
In a short statement, the SNPL said its "determination remains intact".
Pilots are angry about Air France's plans to expand its low-cost operation, Transavia, via regional hubs around Europe.
This is part of wider attempts by the airline to stem losses and compete with budget carriers such as Easyjet and Ryanair that have taken a large chunk of business from more established European carriers.
The company agreed to expand its Transavia operations only within France as a concession to the unions, but insists that it must have the right to vary employment contracts for those working at the low-cost subsidiary.
The pilots want the same contract to be offered to all pilots across all Air France's operations.
Currently, Air France pilots are paid more than Transavia pilots, and they are concerned the airline will replace some Air France flights with Transavia services.