Air France committed to notifying passengers affected by the airline strike via text message or email "to confirm the potential impact on your journey", as long as those contact details were listed in a traveler's reservation.
Air France shares dropped the most in six months after the company said full-year results may fall short of 2017 levels due to rising fuel prices and the strong euro.
Air France-KLM Group tumbled in Paris trading after the resignation of Chief Executive Officer Jean-Marc Janaillac last week threw Europe's biggest airline into disarray, with strikes continuing and senior politicians warning that the company's survival is at stake.
He warned that the state, which owns 14.3 percent of the group, would not serve as a backstop.
"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.
Air France is fell 10% on the stock market Monday after announcing Friday losses of 269 million euros during the first quarter of 2018.
The union's salary demands are "unjustified" and employees must show "responsibility", he said.
A new strike Monday over wage demands, meanwhile, prompted the cancellation of about 15 percent of Air France flights worldwide.
"If Air France does not become more competitive".
A wave of strikes at Air France has so far cost the company 300 million euros.
Last year Italy's Alitalia filed to be put under special administration for the second time in less than a decade, starting a process that will lead to the loss-making airline being overhauled, sold off or wound up.
"Those who think that, whatever happens, the state will come to the rescue of Air France and mop up the losses of Air France are wrong", said Mr Le Maire.
"The absence of any dialogue is clear".
The company had offered a staggered 7 per cent pay increase over four years, with 2 per cent in 2018 and further increases dependent on the airline's financial performance.
Janaillac had been CEO for less than two years, running into the same union resistance to reform as his predecessor.