Book by unknown author following the French state (7)
I believe the answer is:
lebanon
'state' is the definition.
(Lebanon is an example)
'book by unknown author following the french' is the wordplay.
'book' becomes 'b' (abbreviation for book).
'by' says to put letters next to each other.
'unknown author' becomes 'anon' (I've seen this before).
'following' means one lot of letters go next to another.
'the french' becomes 'le' ('the' in French).
'b' next to 'anon' is 'banon'.
'banon' put after 'le' is 'LEBANON'.
(Other definitions for lebanon that I've seen before include "Country with cedars" , "Country associated with cedar trees" , "Neighbour of Israel" , "Beirut's country" , "E. Mediterranean nation" .)