Work unit given backing by illustrious French city (8)
I believe the answer is:
grenoble
'french city' is the definition.
(city in southeastern France)
'work unit given backing by illustrious' is the wordplay.
'work unit' becomes 'erg' (erg is a kind of work unit).
'given backing' says the letters should be written backwards.
'by' means one lot of letters go next to another.
'illustrious' becomes 'noble' (I've seen this before).
'erg' in reverse letter order is 'gre'.
'gre'+'noble'='GRENOBLE'
(Other definitions for grenoble that I've seen before include "City of alpine France, capital of the Isere department" , "French Alpine city" , "City of south-eastern France" , "European city" , "City of SE France" .)