Avoid such heartless article in French (4)
I believe the answer is:
shun
'avoid' is the definition.
(I know that shun is a more specific form of avoid)
'such heartless article in french' is the wordplay.
'heartless' suggests removing the centre.
'article in french' becomes 'un' (an indefinite article in French).
'such' with its middle removed is 'sh'.
'sh'+'un'='SHUN'
(Other definitions for shun that I've seen before include "Avoid, keep away from" , "Parade-ground language" , "Avoid, ignore" , "Keep away from, have nothint to do with" , "attention in the army" .)