Former role here in Paris starts on picket line, extremely shaken, drunk or stoned (4,10)
I believe the answer is:
past participle
'shaken drunk or stoned' is the definition.
(all are examples of past participles)
'former role here in paris starts on picket line extremely' is the wordplay.
'former' becomes 'past' (similar in meaning).
'role' becomes 'part' (synonyms).
'here in paris' becomes 'ici' ('here' in French).
'starts on' indicates taking the first letters.
'extremely' says to hollow out the word (remove centre letters).
'line' with its centre removed is 'le'.
The first letter of 'picket' is 'p'.
'past'+'part'+'ici'+'p'+'le'='PAST PARTICIPLE'
(Another definition for past participle that I've seen is " had, say".)