Irritate majority embracing the French (6)
I believe the answer is:
molest
'irritate' is the definition.
(thesaurus)
'majority embracing the french' is the wordplay.
'majority' becomes 'most' (I've seen this before).
'embracing' indicates putting letters inside.
'the french' becomes 'le'.
'most' enclosing 'le' is 'MOLEST'.
(Other definitions for molest that I've seen before include "Pester in motels" , "Pester unpleasantly" , "Assault in motels" , "Maliciously interfere with" , "Bug" .)