Investigator the French thus thrashed outside (6)

I believe the answer is:

sleuth

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'investigator' is the definition.
(sleuth is a kind of investigator)

I don't understand the remainder of the clue.

(Other definitions for sleuth that I've seen before include "Hustle (anag)" , "Bloodhound" , "Olivier/Caine film" , "See detective" , "A detective like Sherlock - given to hustle" .)

I've seen this clue in The Sun.

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