The chief executive raised the stakes Friday after weeks of strikes by pilots and other workers, warning he will quit if employees reject the company's latest offer on wages.
Jean-Marc Janaillac, 65, has called a company-wide vote at its Air France unit on the proposed seven percent raise over the next four years, with the results expected at 6:00 pm (1600 GMT).
But unions say that's not enough after wage freezes imposed since 2012 as part of Air France's efforts to return to solid profits, and want a 5.1 percent raise this year.
They began a 13th day of intermittent strikes Friday, prompting the cancellation of one-quarter of flights on average.
The move coincided with Air France-KLM's release of first-quarter earnings, which showed a net loss of 269 million euros ($322 million), weighed down by three days of strikes during the period which cost about 25 million euros per day.
The group warned the strike would shave at least 300 million euros off its operating profit for the full year, pulling the earnings "notably below" last year's 1.9 billion euros.
But Janaillac appears to be betting that union resolve is wavering, with just 21.5 percent of pilots participating in Friday's strike, compared with 33 percent when it began in February.
The French government, which owns a minority stake in the group, is watching the situation closely given the general atmosphere of discontent roiling the country, with rail workers, public servants and students also protesting a wide-ranging reform drive.
French Prime Minister Edouard Philippe has hailed Janaillac's "courageous" decision while calling on both sides "to assume their responsibilities".
If employees reject the latest offer, "I would urge everyone to fasten their seat belts because in my opinion, the turbulence won't be light," Philippe told Europe 1 radio last week.
Unions themselves are divided in the standoff, so even if employees do accept management's offer, it might not be ratified anytime soon.
"If the deal is rejected... we'll have a major crisis", said Beatrice Lestic of the moderate CFDT union, which is not taking part in the strike.
She said the strike might be called off, however, "because we wouldn't have a boss to negotiate with."
She said her union along with the CFE-CGC would probably sign the deal, "but that's not enough, we would need a third union" in order to secure a majority.
Other unions representing pilots as well as cabin and ground crews say they deserve "their share of the pie" after years of belt-tightening, which saw Air France post solid results for 2017.
Management counters that its finances remain fragile as it faces stiff competition from carriers in the Gulf as well as from aggressive low-cost operators in Europe.
It says Air France's operating margin of 555 million euros still lags behind that of the 910 million euros at KLM, and "still far behind those of many other rivals".
Janaillac was named chief executive in 2016 with a mandate to ease tensions after years of strikes and labour disputes -- including a notorious 2015 incident when two executives had their shirts torn off while escaping workers protesting plans to cut nearly 3,000 jobs.
The company launched its own low-cost airline, Joon, in 2017, shortly after Janaillac unveiled his own restructuring plan, ambitiously titled "Trust Together".