Rubbish initially carried in one French vessel (3)
I believe the answer is:
urn
'vessel' is the definition.
(urn is a type of container)
'rubbish initially carried in one french' is the wordplay.
'initially' indicates taking the first letters.
'carried in' means one lot of letters goes inside another.
'one french' becomes 'un' ('one' in French).
The initial letter of 'rubbish' is 'r'.
'r' placed within 'un' is 'URN'.
(Other definitions for urn that I've seen before include "Large vase for funeral ashes" , "Large pot for making tea" , "Ashes trophy" , "Large ornamental vase" , "A large vase, perhaps for holding ashes" .)