The French socialist leader's not so much! (4)
I believe the answer is:
less
'not so much' is the definition.
(thesaurus)
'the french socialist leader's' is the wordplay.
'the french' becomes 'les' (les is the in french**).
'leader's' says to take the initial letters (I've seen 'leaders' mean this).
The initial letter of 'socialist' is 's'.
'les'+'s'='LESS'
(Other definitions for less that I've seen before include "Comparatively little" , "Wanting" , "Minus; not so much" , "Comparative of 'a little'" , "Fewer; minus" .)