On Friday, Air France-KLM CEO Jean-Marc Janaillac handed in his resignation to the executive board after the staff rejected a final pay offer from him.
Mr Janaillac is not the first Air France executive to suffer at the hands of its unions.
"If Air France does not make the necessary competitiveness efforts that will allow this national flagship to be at the same level as Lufthansa or other major global airlines, Air France will disappear", said Bruno Le Maire, France's finance minister, in an interview with BFMTV on Sunday.
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 company also had to face the resignation of Jean-Marc Janaillac, president of the group.
Had it been agreed, the pay deal which was put to Air France staff on April 20 would have given them a 7% pay increase over four years including a 2% raise in 2018.
According to the Washington Post, Janaillac resigned Friday evening after workers rejected the company's latest wage proposal.
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He also oversaw the launch of Joon, a low cost subsidiary of Air France, and growth in its maintenance business.
Air France warned that industrial action would continue to affect its services today and tomorrow.
Mr Le Maire told French news channel BFM TV: "I call on everyone to be responsible: crew, ground staff, and pilots who are asking for unjustified pay hikes".
A new strike Monday over wage demands, meanwhile, prompted the cancellation of about 15 percent of Air France flights worldwide.
Air France-KLM reported a net loss of €269m (£238m) in the first quarter of the year.
The number of striking workers appears to be slightly declining as the airline enters its 14th day of walkouts this year, but the labour action has already cost the company more than 300 million euros (£260 million) in a matter of weeks.
"If Air France does not become more competitive".