In the sentence "I must decide which English course to take," is "which English course to take" a noun clause?

I am hesitating to call it a noun clause because there is no conjugated verb (only the verbal "to take"). I am thinking that "which English course to take" is actually an infinitive phrase acting as the direct object.

If you rearrange the sentence, "I must decide to take which English course," this makes a bit of sense to me if you treat "which" as only an adjective and not a subordinating conjunction.

Is this correct, or is it actually a noun clause?

I must decide [which English course to take].

Preliminary point: there's no such thing as a noun clause. The classification of finite subordinate clauses is based on their internal form rather than spurious analogies with the parts of speech.

In your example, the bracketed infinitival clause is a subordinate interrogative clause (embedded question) functioning as complement of the verb "decide". The meaning is deontic, as if the modal auxiliary verb "should" were included, c.f. I must decide which English course I should take.