British Airedale angrily biting backside of Cocteau, French poet (10)
I believe the answer is:
baudelaire
'french poet' is the definition.
(I've seen this before)
'british airedale angrily biting backside of cocteau' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'angrily' indicates an anagram (I've seen this in other clues).
'biting' indicates putting letters inside (some letters bite or swallow others).
'backside of' indicates one should take the final letters.
The last letter of 'cocteau' is 'u'.
'b'+'airedale'='bairedale'
'bairedale' anagrammed gives 'badelaire'.
'badelaire' placed around 'u' is 'BAUDELAIRE'.
(Another definition for baudelaire that I've seen is " French poet and critic, d. 1867 - audible ear (anag)".)