Make unintelligible boast about the French (6)
I believe the answer is:
garble
'make unintelligible' is the definition.
(thesaurus)
'boast about the french' is the wordplay.
'boast' becomes 'brag' (synonyms).
'about' says the letters should be written in reverse.
'the french' becomes 'le' ('the' in French).
'brag' back-to-front is 'garb'.
'garb'+'le'='GARBLE'
(Other definitions for garble that I've seen before include "Indistinct speech" , "Corrupt" , "jumble" , "Distort text or its meaning" , "Transmit in distorted version" .)