Recess husband found in French city (5)
I believe the answer is:
niche
'recess' is the definition.
('niche' can be a synonym of 'recess')
'husband found in french city' is the wordplay.
'husband' becomes 'h'.
'found in' is an insertion indicator.
'french city' becomes 'nice'.
'h' placed inside 'nice' is 'NICHE'.
(Other definitions for niche that I've seen before include "Position well suited to the occupier" , "Speciality" , "Select place in market" , "Particularly well suited position" , "Shallow recess in a wall" .)