The payroll reduction could result in outright firings, they said, which would be a first for the company. In the past, Airbus has cut jobs by not replacing departing staff.
The coming job cuts would mostly affect Airbus's operations in Suresnes, near Paris, and in Ottobrunn, near Munich, the unions said. Some jobs would also go in Marignane in the Marseille region.
The CFTC union said in a statement that Airbus management had already flagged 780 job cuts. But the FO and CFE-CGC union added that an announcement of hundreds of further job cuts could come as early as tomorrow.
An Airbus spokesman called the figures "speculation", adding the company would not make any further statement while negotiations with unions were ongoing.
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Airbus's restructuring project, called Gemini, aims to merge the company's commercial aircraft division Airbus SAS with the Airbus Group SAS into a new entity, Airbus Group, by the summer of 2017.
Airbus currently employs close to 140,000 people worldwide, including subsidiaries, of whom 55,000 work directly for the Airbus aircraft division.
The company has cut jobs before, notably in 2007 and 2008, but only through voluntary redundancies, retirement or redeployment within the company.
Its helicopter division has been suffering from a weak market, the company has had to set aside nearly two billion euros of provisions to cover the cost of its military A400M model and its A380 flagship has been slow to take off commercially.
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