Relative close to Rene in French city (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'close to rene in french city' is the wordplay.
'close to' suggests the final letters (the 'close' to the word).
'in' is an insertion indicator.
'french city' becomes 'nice' (Nice is a French city).
The last letter of 'rene' is 'e'.
'e' placed within 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "member of different generation" , "Brother's daughter" , "Brother's girl" , "Family relative" , "A sibling's child" .)