I'm after the French fabric (4)
I believe the answer is:
lame
'fabric' is the definition.
(lame is a kind of fabric)
'i'm after the french' is the wordplay.
'i'm' becomes 'me' (both refer to the person speaking or writing).
'after' says to put letters next to each other.
'the french' becomes 'la' ('the' in French).
'me' after 'la' is 'LAME'.
(Other definitions for lame that I've seen before include "Thin plate" , "Halt" , "(Of an excuse) unconvincingly feeble" , "game" , "Rubbish" .)