Disadvantage of French river this person’s admitted (9)
I believe the answer is:
detriment
'disadvantage' is the definition.
(I've seen this in another clue)
'of french river this person's admitted' is the wordplay.
'of french' becomes 'de' ('of' in French).
'river' becomes 'trent' (River Trent).
'this person's' becomes 'I'm' ('I am' - 'this person' means the crossword set).
'admitted' indicates putting letters inside.
'trent' going around 'im' is 'triment'.
'de'+'triment'='DETRIMENT'
(Other definitions for detriment that I've seen before include "State of being harmed or damaged" , "Damage, loss" , "Harm, damage" , "Possible loss" , "hurt" .)