Hesitate to be terribly rude about 'monsieur' (5)
I believe the answer is:
demur
'hesitate' is the definition.
(thesaurus)
'terribly rude about monsieur' is the wordplay.
'terribly' is an anagram indicator.
'about' is an insertion indicator.
'monsieur' becomes 'm'.
'rude' anagrammed gives 'deur'.
'deur' enclosing 'm' is 'DEMUR'.
'to be' acts as a link.
(Other definitions for demur that I've seen before include "Raise scruples" , "Hesitation" , "Waver" , "Protest mildly, show reluctance" , "Take exception (to)" .)