In France, she's overwhelmed by part that's shot (6)
I believe the answer is:
pellet
'that's shot' is the definition.
(synonyms)
'in france she's overwhelmed by part' is the wordplay.
'in france she' becomes 'elle' ('she' in French).
'overwhelmed by' indicates putting letters inside (inserted letters get absorbed or overwhelmed).
'part' becomes 'pt' (abbreviation).
'elle' placed into 'pt' is 'PELLET'.
(Other definitions for pellet that I've seen before include "It may be fired" , "Little ball, piece of shot" , "Lightweight bullet" , "Mass of bones and feathers from bird" , "Small round ball" .)