A piloting assistance system for an aircraft during manual piloting is provided. The piloting assistance system includes a monitoring module, configured to compare an acceleration of the aircraft to an authorized acceleration that depends on a speed of the aircraft, an acceleration control module, able to be switched between an activated state and a deactivated state, and configured so as, in the activated state, excluding the deactivated state, to generate a control signal of at least one control device of the acceleration of the aircraft to push the acceleration of the aircraft toward the authorized acceleration range, in order to keep or push the speed of the aircraft in a predefined usage speed range, the monitoring module being configured to activate the acceleration control module when the acceleration of the aircraft is not comprised in the authorized acceleration range.