Assert without proof everyone European has good English (6)
I believe the answer is:
allege
'assert without proof' is the definition.
(I've seen this before)
'everyone european has good english' is the wordplay.
'everyone' becomes 'all' (I've seen this before).
'european' becomes 'e' (abbreviation e.g. EU).
'has' is a charade indicator (letters next to each other).
'good' becomes 'g' (abbreviation).
'english' becomes 'e' (abbreviation).
'all'+'e'+'g'+'e'='ALLEGE'
(Other definitions for allege that I've seen before include "Assert - maintain" , "Aver - maintain" , "Declare or assert without proof" , "Assert, state without proof" , "Swear" .)