The French government has a 14 percent stake in Air France-KLM, in turmoil after its CEO said on Friday he was stepping down when staff rejected a pay deal, but Le Maire said the state was not there to bail out the carrier.
Staff and management at the carrier have been locked in a dispute over pay since February.
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.
The vote came as workers began a 13th day of intermittent strikes Friday, prompting the cancellation of a quarter of flights on average. Zacks Investment Research upgraded Air France-KLM from a "hold" rating to a "buy" rating and set a $18.00 target price for the company in a research note on Thursday, January 11th.
"There is inevitably some pain for staff when structural changes are made, but once that is dealt with, you're left with a much healthier company", said aviation consultant John Strickland.
The company had revenue of $7.34 billion during the quarter, compared to the consensus estimate of $8 billion. analysts expect that Air France-KLM will post 2.71 earnings per share for the current fiscal year.
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.
Ahead of the vote, French Prime Minister Edouard Philippe had urged both sides "to assume their responsibilities".
In the Friday vote, 55.44 percent of votes cast were against the offer, on an 80.33 percent participation rate.
Unions said they would be sticking with plans to strike on May 7 and May 8.
In a statement the company said he would officially resign on May 9.
Air France-KLM chief Jean-Marc Janaillac "This is an enormous mess that will only put a smile on the faces of our competitors", Mr Janaillac told a news conference.