A Parisian, over barrel, deserted flat? (7)

I believe the answer is:
untuned
'flat?' is the definition.
(thesaurus)
'a parisian over barrel deserted' is the wordplay.
I cannot really understand how this works, but
'barrel' could be 'tun' (tun is a kind of barrel) and 'tun' is found in the answer.
'deserted' could be 'd' and 'd' is found in the answer.
'a parisian' could be 'une' ('a' in French) and 'une' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for untuned that I've seen before include "(Of piano) not adjusted" , "With no fixed pitch" .)
