Disagree with European without causing offence (6)

I believe the answer is:

demure

I'm a little stuck... Click here to teach me more about this clue!

'without causing offence' is the definition.
I can't tell whether this defines the answer.

'disagree with european' is the wordplay.
'disagree' becomes 'demur' (I've seen this before).
'with european' becomes 'e' (abbreviation e.g. EU. I am not sure about the 'with' bit.).
'demur'+'e'='DEMURE'

Can you help me to learn more?

(Other definitions for demure that I've seen before include "Chaste" , "Mild" , "Staid" , "Prim, coy" , "Reserved, modest, shy" .)

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.