That Parisian behind investigator's animosity (5)
I believe the answer is:
pique
'animosity' is the definition.
(I've seen this before)
'that parisian behind investigator's' is the wordplay.
'that parisian' becomes 'que' ('that' in French).
'behind' says to put letters next to each other.
'investigator' becomes 'PI' (private investigator).
'que' put after 'pi' is 'PIQUE'.
(Other definitions for pique that I've seen before include "Hurt feelings" , "Resentful feeling" , "Offence taken" , "Stimulate (someone's interest)" , "Animosity" .)