Relative close to bridge in French city (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'close to bridge in french city' is the wordplay.
'close to' says to take the final letters (the 'close' to the word).
'in' means one lot of letters goes inside another.
'french city' becomes 'nice' (Nice is a French city).
The final letter of 'bridge' is 'e'.
'e' going inside 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "member of different generation" , "Brother's daughter" , "Brother or sister's daughter" , "A sibling's daughter" , "Family relation" .)