Eccentric French composer wrapping clear thin fabric (9)
I believe the answer is:
satinette
'thin fabric' is the definition.
(satinette is a thin fabric)
'eccentric french composer wrapping clear' is the wordplay.
'eccentric french composer' becomes 'Satie' (French composer Erik Satie, 1866-1925).
'wrapping' is an insertion indicator.
'clear' becomes 'nett' (similar in meaning).
'satie' going around 'nett' is 'SATINETTE'.
(Other definitions for satinette that I've seen before include "material" , "stuff!" , "Glossy fabric" .)