French city is seriously annoying (6)
I believe the answer is:
angers
I believe this is a double definition.
'french city' is the first definition.
(Angers is a city in France)
'is seriously annoying' is the second definition.
(to anger someone is to be very annoying)
(Other definitions for angers that I've seen before include "Riles" , "gets hot" , "Maine city" , "Outrages" , "home of French citizens" .)