Object of French flipping strange (5)
I believe the answer is:
demur
'object' is the definition.
(to demur is to object to something)
'of french flipping strange' is the wordplay.
'of french' becomes 'de' ('of' in French).
'flipping' says the letters should be written in reverse.
'strange' becomes 'rum' (synonyms).
'rum' back-to-front is 'mur'.
'de'+'mur'='DEMUR'
(Other definitions for demur that I've seen before include "Take exception (to)" , "Protest mildly, show reluctance" , "Cavil, dispute" , "Protest or disagree mildly" , "Raise objections" .)