Yes, I'd say A European...Eu sounds like a consonant, "Yuropean". If we chose An with European, we'll pronounce it this way, Aneuropean...It just doesn't sound right.
I agree with Trish21.
Her explanation is correct because the sound is that of a consonant (you)
not (an).
I have also been teaching and have been giving this question as an example when teaching Articles in class. My students speaks mainly Malay, Chinese or Tamil. You can imagine what I am going through and they are all blind and some never went to school at all.