The protest vote, known as a "droit d'alerte", came as union leaders and Air France management met on Thursday to discuss the carrier's plans.
It was the first meeting between the two parties since earlier this month when a group of angry Air France employees grabbed two company executives outside Charles de Gaulle airport, tearing their clothes.
The company suspended five workers in connection with that attack.
At that time Air France had announced a plan to lower costs that included cutting 2,900 jobs through 2017.
On Thursday, management proposed to cut 1,000 of those positions through a voluntary retirement scheme in 2016 and said it would reconsider cutting the other 1,900 jobs.
But workers say so far management has not provided them with any guarantees.
Union leaders say Air France management is required by law to provide employees with a detailed breakdown of the number of jobs the company plans to cut, sector by sector.
They say that, as part of their formal protest, a consultancy firm will press Air France bosses for detailed information on the company's restructuring plans.
The union has also called on workers to demonstate outside the French parliament.
Meanwhile, talks between the two sides were due to continue through Friday.