The French start to strike? Not so much (4)
I believe the answer is:
less
'not so much' is the definition.
(thesaurus)
'the french start to strike?' is the wordplay.
'the french' becomes 'les' (les is the in french**).
'start to' indicates taking the first letters.
The first letter of 'strike' is 's'.
'les'+'s'='LESS'
(Other definitions for less that I've seen before include "more, as they say" , "A smaller amount" , "Fewer in number" , "Comparatively little" , "Fewer; minus" .)