Complained that Monsieur had done a lift (6)
I believe the answer is:
moaned
'complained' is the definition.
(I've seen this in another clue)
'monsieur had done a lift' is the wordplay.
'monsieur' becomes 'm' (French abbreviation - like Mr for Mister).
'had' says to put letters next to each other.
'lift' indicates an anagram (I've seen 'lifts' mean this).
'done'+'a'='donea'
'donea' anagrammed gives 'oaned'.
'm'+'oaned'='MOANED'
'that' acts as a link.
(Other definitions for moaned that I've seen before include "A demon (anag.)" , "Made low sound of pain or distress" , "Complained" , "Made low mournful sound as of pain" , "Made low sound of pain - or grumbled" .)