"The consequences of these measures will necessarily influence our financial trajectory and could put us in a difficult cash flow position if we do not react immediately," Zaan said in the letter, first reported by the French business daily Les Echos.
Zaat called on Air France managers to cut back on discretionary spending, including on travel and consultants, and to impose a hiring freeze on all services not directly related to operations.
Furthermore, it will begin a review of plans for investments in technology and facilities.
According to Les Echos, Air France's partner airline KLM has issued a similar directive, including urging employees to use up holidays while flights are being cut back.
Air France, KLM and other airlines have temporarily suspended most if not all flights to China, the epicentre of the coronavirus outbreak which has now killed over 2,700 people and infected more than 80,000.
Last week, the International Air Transport Association said it estimates airlines operating in the Asia-Pacific region stand to lose a combined $27.8 billion in revenue this year due to the coronavirus crisis.
Other airlines such as Germany's Lufthansa have also announced measures to cope with the impact.
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