how was the existing system of justice altered during the enlightenment?

The answer is People reconsidered the administration of law and redefined corrections.
During this period the classical school of criminology emerged, with its insistence on a rational link between the gravity of the crime and the severity of the punishment.
The social contract and utilitarianism emphasized limitations ont he government and the need to erect a system of punishments so that people would be deterred from crime.