A fan module for an aircraft turbine engine, this module comprising a fan and an electrical machine, such that the electrical machine is coaxially mounted downstream of the fan and comprises a rotor coupled to rotate with the fan and an annular member with generally C-shaped axial cross-section, the opening of which is axially orientated and receives the rotor, this member comprising a radially outer portion forming a stator, and a radially inner portion forming a support for bearings guiding the rotor.