The company, which will report first half results in August, declined to comment on the figure.
It lost many of its customers last year after having being criticised on the quality of its network.
Billionaire Patrick Drahi, who controls SFR's parent company Altice (>> Altice A), had promised when Altice bought the telecoms operator two years ago, not to touch the company's headcount until mid-2017. A spokesman confirmed SFR would stick to that.
Drahi built up his cable and telecommunications group through debt while promising investors that he could generate more cash under his ownership.
In June, the businessman told reporters in New York that SFR was overstaffed. SFR's boss Michel Combes told lawmakers at the National Assembly the same month that the group will adjust its workforce to reflect prevailing market conditions.
"Drahi is very much able to cut costs, the market knows it," said Agathe Martin, an analyst at Exane BNP Paribas. "But what the market wants to know today is what he plans to do to retain customers to generate more revenue."
SFR's rivals have also had to reduce costs over the last four years following the arrival of Iliad's low-cost Free Mobile services in 2012, which triggered a price war, whose effects are still be felt today by the industry.
Bouygues (>> Bouygues) Telecom has already reduced its headcount by about 2,000 jobs to 6,500 since 2013 through two voluntary departures plans. France's leading telecoms operator Orange (>> ORANGE SA) said it would not replace some of its employees going on retirement.
(Editing by Richard Lough, Astrid Wendlandt and Alexandra Hudson)
By Gwénaëlle Barzic and Mathieu Rosemain