What’s wrong with “… enforce that …”

Solution 1:

Ensure and enforce are indeed similar in that they are both transitive (i.e. they take a direct object), but not all transitive verbs are equal. Enforce only takes a noun or noun phrase (such as the rules) as its direct object, while ensure is more versatile (from a grammatical standpoint): while it can take a noun or noun phrase, it can also take a content clause (also called complement clause or that-clause; such as that the rules are followed) as its object. This has been established by usage and convention, and it is rare to see enforce paired with that. In this case, convention dictates the grammatical constraints, and therefore it is grammatically incorrect to use a that-clause as the object of certain verbs (such as enforce). Ngrams shows relative usages:

As you mention, you could replace enforce with ensure:

People then create laws to ensure that these regulations are being followed.

Or, if you want to keep the strength of enforce, you would need to change the direct object from a content clause to a noun phrase:

People then create laws to enforce these regulations.

Solution 2:

Apart from the fine answers already given here that focus on grammaticality, it bears noting that laws cannot enforce anything- they can merely prescribe and proscribe, but not enforce.
In fact they themselves require enforcement- thus the existence of "law enforcement officers".