Primarily, come here in Cannes, the height of fashion (4)
I believe the answer is:
chic
'fashion' is the definition.
(thesaurus)
'primarily come here in cannes' is the wordplay.
'primarily' suggests taking the first letters.
The initial letters of 'come here in cannes' is 'CHIC'.
'the height of' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for chic that I've seen before include "Fashionably elegant" , "Stylishness, elegance" , "In vogue" , "Trendy" , "Modish" .)