Good school subject to follow in French class (5)
I believe the answer is:
'class' is the definition.
(genre can mean a class or type)
'good school subject to follow in french' is the wordplay.
'good' becomes 'g' (abbreviation).
'school subject' becomes 'RE' (Religious Education).
'to follow' is a charade indicator (letters next to each other).
'in french' becomes 'en' ('in' in French).
're' after 'en' is 'enre'.
(Other definitions for genre that I've seen before include "Category of literature" , "Literary type, species" , "Particular style of art or literature, may be green" , "Style/category of art" , "Style (of art/literature)" .)