Plant makes Frenchman sick (4)
I believe the answer is:
mill
'plant' is the definition.
(mill is a kind of plant)
'frenchman sick' is the wordplay.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'sick' becomes 'ill' ('ill' can be a synonym of 'sick').
'm'+'ill'='MILL'
'makes' is the link.
(Other definitions for mill that I've seen before include "Grind (grain)" , "Flour is produced here" , "Plant with facilities for manufacturing" , "Race a moving influence on this" , "There's an old one by the stream, Nellie Dean" .)