Cool French detective's taking time to visit (7)
I believe the answer is:
inflict
'to visit' is the definition.
('inflict' can be a synonym of 'visit')
'cool french detective's taking time' is the wordplay.
'cool' becomes 'in' ('in' can mean fashionable or cool).
'french detective' becomes 'flic' (French term for a police officer).
'taking' is a charade indicator (letters next to each other).
'time' becomes 't' (abbreviation).
'in'+'flic'+'t'='INFLICT'
(Other definitions for inflict that I've seen before include "Impose something unpleasant, perhaps a wound" , "Impose (painfully) upon" , "Mete out (punishment)" , "Impose (something painful on someone)" , "Lay on" .)