Small island near France - the very thing for someone demanding solitude (6)
I believe the answer is:
hermit
'someone demanding solitude' is the definition.
(a hermit lives alone)
'small island near france the very thing' is the wordplay.
'small island near france' becomes 'Herm' (one of the Channel Islands).
'the very thing' becomes 'it'.
'herm'+'it'='HERMIT'
'for' acts as a link.
(Other definitions for hermit that I've seen before include "Anchorite or religious recluse" , "One lives in solitude for religious reasons" , "Person like Peter" , "Solitary dweller" , "Liver in solitude" .)