An aircraft turbine engine includes a gas generator and a fan arranged upstream of the gas generator and configured to generate a main gas flow, of which one portion flows in a stream from the gas generator to form a primary flow, and of which another portion flows in a stream around the gas generator to form a secondary flow. The gas generator includes a low pressure body having a rotor driving the fan by means of a crown of a mechanical planetary reduction gear. The turbine engine further includes an electrical machine mounted coaxially around the reduction gear and having a rotor rotated by the crown of the reduction gear, and a stator extending around the rotor of the electrical machine.