Superfluity embarrassed duke in posh French city (10)
I believe the answer is:
redundancy
'superfluity' is the definition.
(redundancy is a kind of superfluity)
'embarrassed duke in posh french city' is the wordplay.
'embarrassed' becomes 'red' (I've seen this before).
'duke' becomes 'd'.
'in' means one lot of letters goes inside another.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-u).
'french city' becomes 'nancy' (I've seen this before).
'u'+'nancy'='unancy'
'd' put within 'unancy' is 'undancy'.
'red'+'undancy'='REDUNDANCY'
(Other definitions for redundancy that I've seen before include "Loss of job" , "Dismissal" , "Surplus, especially in one's job!" .)