On Monday, the company's shares went into tailspin on the Paris stock exchange on Monday, falling by 13 percent after the French finance minister's statements, and following the resignation of the company's CEO on Friday.
Shares were down almost 10 per cent as investors continued to lose faith in the airline, which has been battered by three months' worth of strikes over pay and working conditions.
The firm's CEO Jean-Marc Janaillac announced his resignation on Friday after staff at the carrier's French operations rejected a pay deal aimed at ending months of walkouts.
The offer was open until 4 May, but did not receive the number of signatures required for it to be implemented.
The French government, which owns 14.3 per cent of the company, said Air France needed to reform or its survival would be at stake.
The stock dropped as much as 14 per cent, the most since 2002, on Monday, when Europe's biggest airline was forced to scrap 15 per cent of its flights and said even more would be cancelled on Tuesday due to a series of strikes that began in February.
Air France-KLM posted a first quarter operating loss of €118 million ($141 million) last week, attributing €75 million of that loss to the strike impact.
Janaillac will formally resign at a Board of Directors' meeting on May 9, the company said, adding that "it will be their responsibility to take the appropriate measures to ensure the continuity of the group and Air France during the transition period".
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Societe Generale analysts warned the weaker earnings performance could lead to a rift between Air France and its profitable Dutch partner, KLM.
France's economy minister on Sunday warned that the survival of Air France was now in the balance.
"The state is not there to pay off debts, come to the rescue of companies that would not make the necessary efforts of competitiveness", he told the French news channel BFMTV.
Air France-KLM reported a net loss of €269 million ($321 million) in the first quarter of the year.
He warned that the state, which owns 14.3 percent of the group, would not serve as a backstop.
"If Air France does not become more competitive".
This is in sharp contrast to its performance past year, when the shares rose 160 percent as Janaillac initiated reforms to restructure and improve the finances of its French brand, said Roche Brune Asset Management's Laverne.
Staff and management at the carrier have been locked in a dispute over pay since February.