John or Paul perhaps got the best of the French (6)
I believe the answer is:
beatle
'john or paul perhaps' is the definition.
(John Lennon and Paul McCartney were Beatles)
'got the best of the french' is the wordplay.
'got the best of' becomes 'beat' (both can mean defeated).
'the french' becomes 'le' ('the' in French).
'beat'+'le'='BEATLE'
(Other definitions for beatle that I've seen before include "Paul, Ringo, John or George" , "John, Paul or George, say" , "One of the famous four pop musicians, says Paul or John" , "eg Ringo" .)