The harassment reported by Sofoot concerns messages of a sexual nature from union president Noël Le Graët to female employees.
Among other things, examples are mentioned where he invites to dinner and writes that he prefers blondes.
Additional examples of invitations are also covered.
So far, neither Le Graët nor the French federation has made any statement on the matter.
France is the reigning champion of the World Cup and the Nations League.
Le Graët has been confederation chairman since 2011.