University sensitive about good French name (8)
I believe the answer is:
sorbonne
'university' is the definition.
(a university in Paris)
'sensitive about good french name' is the wordplay.
'sensitive' becomes 'sore' ('sore' can be a synonym of 'sensitive').
'about' means one lot of letters goes inside another.
'good french' becomes 'bon'.
'name' becomes 'n' (common abbreviation e.g. on forms).
'bon'+'n'='bonn'
'sore' enclosing 'bonn' is 'SORBONNE'.
(Other definitions for sorbonne that I've seen before include "Non-Boers go over to this French university" , "Famous part of Paris University with literature and science faculties" , "Parisian institution" , "Common name for the University of Paris" , "Parisian university" .)