Unhealthy entering the French industrial city (5)
I believe the answer is:
lille
'industrial city' is the definition.
(I know that Lille is a industrial city)
'unhealthy entering the french' is the wordplay.
'unhealthy' becomes 'i'll' (associated in meaning).
'entering' is an insertion indicator.
'the french' becomes 'le' ('the' in French).
'ill' inserted within 'le' is 'LILLE'.
(Other definitions for lille that I've seen before include "City of northern France, close to Belgium" , "Eurostar stop" , "City of N. France" , "[FRANCOPHOBIA] would prevent you appreciating it" , "European city" .)