Frenchman is sick of local disagreement (4)
I believe the answer is:
mill
'local disagreement' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.
'frenchman is sick' is the wordplay.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'is sick' becomes 'ill' ('ill' can be similar in meaning to 'sick').
'm'+'ill'='MILL'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for mill that I've seen before include "Plant with facilities for manufacturing" , "Race a moving influence on this" , "Grind to a powder or dust" , "Grind (flour)" , "No fun going through this" .)