A turbine engine for a helicopter, the helicopter including a main gearbox, a rotor, and a speed-reducing device housed entirely within the main gearbox of the helicopter while also being connected to the rotor, the turbine engine including a casing, a gas generator with a gas generator shaft, and a free turbine for being driven in rotation by a gas stream generated by the gas generator, the free turbine including a free turbine shaft. When the turbine engine is fastened to the gearbox of the helicopter, the free turbine shaft extends axially into the main gearbox of the helicopter to be connected directly to the speed-reducing device.