Who enforced national laws during the period of the Articles of Confederation?
Each colony had its own long established system of laws and law enforcement.
The end of the American Revolution ended only each colony's duty towards England. As the colonies were founded in the 17th century they first created laws and means for insuring the observance of those laws. Each colony had its own constitution which it used as a basis for its legal system.
From 1783 to 1789 those colonies continued to act as individual governments which were very loosely bound together by the Articles of Confederation. That the colonies became "states" was equivalent to individual country as we often refer to any country in the world, they are also a state.
Our Constitution was designed to strongly bind
together each of these individual states and bring them under a singular authority.