An attachment device for an aircraft engine including a rigid structure and an attachment mechanism of the engine onto the rigid structure. The attachment mechanism includes two thrust take-up connecting rods mechanically connected to a spreader, a connection fitting fixed to the rigid structure to which the spreader is mechanically connected by a junction fitting by a connection pin, and an additional fitting to which the connecting rods, the spreader, and the connection fitting are mechanically connected. A clearance is provided at the mechanical link between the connecting rods and the additional fitting, the link between the additional fitting and the connection fitting being made using the connection pin being inserted laterally, orthogonal to the median plane of the attachment device.