Not so much for the French on the ship (4)
I believe the answer is:
less
'not so much' is the definition.
(I've seen this before)
'the french on the ship' is the wordplay.
'the french' becomes 'le' ('the' in French).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'the ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'le'+'ss'='LESS'
'for' is the link.
(Other definitions for less that I've seen before include "Minus; not so much" , "A smaller amount" , "Smaller in amout or degree" , "In smaller quantity" , "Fewer in number" .)