On Friday 55 percent of the 46,771 Air France employees who voted turned down the offer.
The unions said the increase was too little after six years of pay freezes and demanded a 5.1 percent raise this year.
Staff and management at the carrier have been locked in a dispute over pay since February.
Friday's vote came as workers embarked on a 13th day of strikes, prompting the cancellation of a quarter of flights.
The industrial action has cost the Franco-Dutch airline millions of euros.
Janaillac had been gambling on the strikers' resolve wavering, with just 21.5 percent of pilots participating in Friday's walkout, compared with 33 percent when the stoppages began in February.
A further strike is planned for Tuesday 8 May.
Ministers pay tribute
The French government, which owns a minority stake in the group, has called on both sides to assume their responsibilities.
Janaillac's departure is unlikely to resolve the crisis, leaving unions with nobody to negotiate with.
He is expected to tender his resignation at a board meeting on 9 May.
The board will have to "define the conditions to end the current crisis", Economy Minister Bruno Le Marie and Transport Minister Elisabeth Borne said, adding a tribute to the "courage of Jean-Marc Janaillac and the work he has done to help the group's recovery".
Ahead of the vote, the 65-year-old told journalists he might retire if he was obliged to resign.
"I could. I'm the right age," he commented.
"The CEO of #AirFrance has just invented the fire-your-boss referendum," tweeted hard-left politician Jean-Luc Mélenchon.
He suggested that Guillaume Pépy, the boss of strike-hit rail company SNCF, might like to take up the idea.