correct usage of a and an

Which is correct?
An European mandate
A European mandat

"A European mandate" is correct. ;-)

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.
;-)