Workers voted to halt production following an announcement by Russian owner Alexandre Pougatchev that the title would switch to an online-only version from December. The move would lead to 89 of the 116 jobs being cut.
"The employees of France Soir reject the planned rapid disappearance of the title accompanied by a large number of redundancies," said a statement by workers.
The plan to scrap the paper edition of the newspaper will be considered by the Tribunal de Commerce, which mediates on business disputes.
If the tribunal approves the plan, France Soir will be the first French daily newspaper to abandon its print edition.
France Soir was originally launched in November 1944 by two underground resistance fighters, Robert Salmon and Philippe Viannay.
It was originally published under the title "France Soir - Défense de la France", reverting to just France Soir after the war.
Circulation grew to 1.5 million in the mid-1950s under its famed editor Pierre Lazareff but had already started falling by the 1960s. Successive management changes and relaunches failed to stem falling sales.
The newspaper was relaunched in tabloid format in 1998 and again in 2010 after it was bought by Russian billionaire Alexandre Pougatchev. Its current circulation is around the 60,000 level.
1944 was a bumper year for newspaper launches with Le Monde and Le Parisien also being founded. The oldest surviving national daily in France is Le Figaro which was founded in 1826 under the reign of Charles X.
The most widely-read national newspaper in France is Le Parisien, which also publishes under the title Aujourd'hui en France (Today in France) nationally. Its circulation is 470,000. Le Figaro and Le Monde both have circulations of around 320,000.
The best read newspaper overall in France is regional newspaper Ouest-France which sells around 770,000 copies.