Relative close to collapse in French city (5)
I believe the answer is:
niece
'relative' is the definition.
(niece is a kind of relative)
'close to collapse in french city' is the wordplay.
'close to' suggests the final letters (the close/ending of).
'in' means one lot of letters goes inside another.
'french city' becomes 'nice'.
The last letter of 'collapse' is 'e'.
'e' going into 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "Brother or sister's daughter" , "Daughter of a sibling" , "A sibling's daughter" , "Kinswoman" , "Family girl" .)