Shame of French importing rotten cigars (8)
I believe the answer is:
disgrace
'shame' is the definition.
('disgrace' can be a synonym of 'shame')
'of french importing rotten cigars' is the wordplay.
'of french' becomes 'de'.
'importing' is an insertion indicator.
'rotten' indicates anagramming the letters.
'cigars' with letters rearranged gives 'isgrac'.
'de' placed around 'isgrac' is 'DISGRACE'.
(Other definitions for disgrace that I've seen before include "Cause of shame or dishonour" , "scandalous" , "State of dishonour" , "Dishonour, ignominy" , "Loss of good reputation" .)