The propulsion system includes an internal combustion engine, an electric machine and a double-clutch transmission with a clutch unit and a mechanical gearbox. The gearbox has two coaxial primary shafts intended to be torsionally connected each to a shaft of the internal combustion engine of the motor vehicle by a respective friction clutch of the clutch unit, as well as a secondary shaft and a lay shaft arranged parallel to the two primary shafts. The electric machine is permanently kinematically connected to either of the two primary shafts via a first gear train including a pinion mounted on an output shaft of the electric machine, an intermediate gearwheel mounted on an intermediate shaft and a gearwheel mounted on the primary shaft and acting as driving gearwheel of a second gear train of the gearbox associated to one of the gears, in particular to the second forward gear. The gearbox further includes a casing and the electric machine is inserted and fixed into a seat formed by that casing. An outer surface of a stator of the electric machine forms a spiral-shaped profile which serves as cooling circuit for the electric machine and is closed on the radially outer side by an inner cylindrical surface of the seat, in such a manner that the channels of the cooling circuit are defined between the spiral-shaped profile and the inner cylindrical surface.