Terrible illness rate linked to the French island group (6,8)
I believe the answer is:
lesser antilles
'island group' is the definition.
(I've seen this before)
'terrible illness rate linked to the french' is the wordplay.
'terrible' is an anagram indicator.
'linked to' means one lot of letters go next to another.
'the french' becomes 'les' (plural form of 'the' in French).
'illness'+'rate'='illnessrate'
'illnessrate' is an anagram of 'lesserantil'.
'lesserantil'+'les'='LESSER ANTILLES'
(Other definitions for lesser antilles that I've seen before include "island group" , "group of Caribbean islands" .)