Disclosed is an aircraft turbine engine (10), comprising a gas generator (12) and a fan (14) arranged upstream from the gas generator (12) and configured to generate a gas inlet stream (F), part of which flows into a duct of the gas generator to form a primary stream (36), the turbine engine (10) comprising an electrical machine that is mounted coaxially downstream from the fan (14) and that comprises a rotor (62a) surrounded by a stator (62b) carried by an annular shroud (64), this shroud (64) being surrounded by a casing (40) of the gas generator that defines, with this shroud (64), a section of the flow duct for the primary stream (36), stationary vanes (42, 68) for straightening this primary stream (36) extending into this path.