The probe forms part of a broader investigation into alleged anticompetitive activities within the French industry that also includes TNT Express and FedEx, which has said that the allegations centre on trade association meetings.
Analyst estimates put the fine at anything up to 10% of worldwide turnover (the maximum permitted under French antitrust law), which could mean a £160m fine for the recently privatised Royal Mail Group.
TNT would face a potential fine of up to €670m (£530m) based on its €6.7bn group turnover.
Royal Mail said: "We are currently considering the notice received from the French regulator. Given the early stage of this matter, we cannot yet determine the amount or range of potential loss; however, it is possible that it could be material."
GLS is one of Europe's largest ground-based parcel delivery networks, with operations in 37 countries including France, which accounts for 70% of sales. GLS contributed approximately 17% of Royal Mail Group's £9.5bn turnover last year.
Royal Mail said that it would provide an update "at the appropriate time". The company's shares were trading down marginally at 484.6p at the time of writing; the float price for the shares was 330p, although they opened trading at 430p and reached a 52-week high of 618p.
