I believe there's a subtle difference. As an example: " I have an appointed with my German teacher " can translate to either " Ik heb een afspraak met mijn leraar Duits" --> Meaning that the teacher teaches German, it has nothing to do with his nationality, whereas the same sentence can be translated to " Ik heb een afspraak met mijn Duitse leraar" --> Meaning the teacher is German, he may teach Spanish, or math for that matter.
In this sentence, if you would say: "Ik heb een Engels cursus nodig" I think it should be accepted, as it basically has the same meaning as "Ik heb een cursus Engels nodig".
Please correct me if I'm wrong btw
I think it is like the German teacher (either teaching German or being German) this is the same: Een Engelse Cursus = a course taught in English, but the subject is unimportant. Een cursus Engels = a language course to learn how to speak in English. But all Dutch people do this wrong as well, so don't bother remembering this. But it is the reason why 'Engels' is after 'cursus' here.