Annoys the French following demand (7)
I believe the answer is:
needles
'annoys' is the definition.
(I've seen this before)
'the french following demand' is the wordplay.
'the french' becomes 'les' ('the' in French).
'following' says to put letters next to each other.
'demand' becomes 'need' (synonyms).
'les' after 'need' is 'NEEDLES'.
(Other definitions for needles that I've seen before include "Is annoying" , "Rocks off Isle of Wight" , "They may play LPs" , "Western point of the Isle of Wight" , "Pine leaves" .)