Choice of the French dividing piece (9)
I believe the answer is:
selection
'choice' is the definition.
(synonyms)
'the french dividing piece' is the wordplay.
'the french' becomes 'le'.
'dividing' is an insertion indicator.
'piece' becomes 'section' (section is a kind of piece).
'le' put into 'section' is 'SELECTION'.
'of' acts as a link.
(Other definitions for selection that I've seen before include "Choice, pick" , "Horse tipped for betting" , "Act of choosing" .)