This writer's found in the French capital (4)
I believe the answer is:
lima
'capital' is the definition.
(capital of Peru)
'this writer's found in the french' is the wordplay.
'this writer's' becomes 'I'm' (referring to the person writing the clues).
'found in' is an insertion indicator.
'the french' becomes 'la' (one of the French words for 'the').
'im' going into 'la' is 'LIMA'.
(Other definitions for lima that I've seen before include "Mail to Peru's capital" , "South American capital" , "Send mail out to S America" , "Mail to Peru'd capital" , "Edible bean; capital city" .)