The French Prime Minister and Air France on Thursday both issued warnings over the damage caused to the airline by workers striking over pay.
The dispute has so far cost Air France some €300 million ($365 million).
Air France is balloting staff over its offer of a 7 percent pay rise over four years after unions rejected the proposal as too modest.
Three pilot unions on Thursday called for more strikes over the May 3-8 period – a move condemned by the airline as putting its economic situation “even more at risk”.
Prime Minister Edouard Philippe said Air France faced significant “turbulence” if it lost its battle with unions. The French state holds 17.6 percent of the Air France KLM group.
Air France KLM Chairman and Chief Executive Jean-Marc Janaillac has said it would be hard for him to stay if staff voted against the offer, and he issued an apology to the airline’s customers in a statement on Thursday.
“I have complete faith in the desire of Air France staff to put an end to this destructive situation for our airline,” added Janaillac in his statement.
Philippe said Janaillac had shown “courage” by putting his job on the line but warned that a negative vote could further harm the company.
“If the consultation did not produce the results he hoped for and he took the consequences, everyone should fasten their seat belts because the turbulence will not be minor,” he told Europe 1 radio. “A company that loses its boss in these conditions is not well placed to face the future.”
The industrial action, affecting about 30 percent of Air France flights, has coincided with French railway strikes over the last month, resulting in widespread travel disruption.
SNCF workers have launched a series of protests against reform plans by President Emmanuel Macron’s government, designed to stem the state-owned railway’s losses and cut debt.
Air France KLM shares went down by more than 1 percent in early session trading on Thursday.