A system for aiding the piloting of an aircraft during a runway approach includes an information source that provides information relating to the aircraft and its environment. A computation unit determines, with the aid of information provided by the information source, an energy reference profile having a trajectory reference profile and a speed reference profile that allows the aircraft to regain a stabilized approach trajectory, if it follows the reference profile. A monitor verifies that the aircraft is following the reference profile. An indicator supplies the pilot with piloting indications for piloting the aircraft so as to follow the reference profile.