The airline said it would only guarantee half of its long-distance flights. In addition, 30 percent of its shorter flights could be canceled, Radio France International reported.
The work action has begun to affect other airlines. Discount carrier easyJet canceled several flights to France Monday.
Workers are striking to protest a law that passed in the lower house in January that would restrict how strikes can be managed.
One provision of the bill the unions disagree with would make it illegal to strike without first giving 48 hours notice.
Celebrity Families of 2014 [PHOTOS]