The group, one of the world's biggest catering companies alongside Britain's Compass, said it planned to propose all possible measures to limit the impact - particularly through voluntary transfers to its other activities in France.
"I hope all the measures we take will be sufficient and will allow us to employ people again when we return to growth," chief executive Denis Machuel told reporters.
He added that Sodexo - which provides catering for businesses, government agencies, hospitals, schools and events - had already transferred thousands of employees from closed posts such as retirement homes and had identified some 600 open posts in France.
Sodexo announced the job cuts on Tuesday, saying they would represent less than 7% of its workforce and mainly affect its corporate services operation.
Restructuring costs during its 2020 fiscal year more than quadrupled to 191 million euros as government support schemes across its regions come to an end.
The firm forecast a 20-25% revenue slump for the six months ending February 2021 compared to the same period of 2020, as well as a free cash flow hit of 250 million euro ($295.48 million) from restructuring costs, payment delays and reimbursement of Olympic Games hospitality packages.
Sodexo's core profit fell 50% for the fiscal year ended Aug. 31 on 11% lower revenue, beating analysts' expectations.
Machuel said he remained confident in Sodexo's guidance after France announced a return into lockdown on Wednesday night.
Sodexo decided not to propose a dividend for its 2020 fiscal year.
(Story refiles to clarify constant rates in 3rd last para)
(Reporting by Sarah Morland in Gdansk, Editing by Sherry Jacob-Phillips and Tomasz Janowski)