The use of the indefinite article is based on sound not spelling, so European begins with a consonant sound, not a vowel:
An egg (vowel sound)
A European egg (consonant sound)
The same is true of words beginning with U:
A university
An umbrella
It also happpens accasionally with the letter O:
A one-day cricket match.
You can have AN before a consonant:
She's taking an MA at Oxford University.
;-)