Back alien at French Island, being of upper class (5)
'class' is the definition.
(elite is a kind of class)
'back alien at french island being of upper' is the wordplay.
'back' shows that the letters should be reversed in order.
'alien' becomes 'et' (extra terrestrial).
'at' says to put letters next to each other (I've seen this in other clues).
'french island' becomes 'ile' ('island' in French).
'being of upper' says the letters should be written backwards (I've seen 'up' mean this (in down clue: letters go upwards)).
'et' in reverse letter order is 'te'.
'ile' reversed gives 'eli'.
'te' after 'eli' is 'ELITE'.
(Other definitions for elite that I've seen before include "Exclusive group", "type in pool?", "twelve pitch in the office", "Privileged or posh group", "Best, privileged, group".)