To go under makes French leader feel ill (4)
I believe the answer is:
fail
'to go under' is the definition.
(I've seen this in another clue)
'french leader feel ill' is the wordplay.
'leader' suggests taking the first letters.
'feel ill' becomes 'ail' (I've seen this in another clue).
The first letter of 'french' is 'f'.
'f'+'ail'='FAIL'
'makes' acts as a link.
(Other definitions for fail that I've seen before include "Go bankrupt" , "Let down" , "Come to naught" , "collapse" , "Neglect (to do something)" .)