Problem backing the French — quite without oomph — in raunchy US show (9)
I believe the answer is:
burlesque
'raunchy us show' is the definition.
(sexual performance in the US)
'problem backing the french quite without oomph' is the wordplay.
'problem backing' becomes 'bur' (I can't justify this - if you can you should believe this answer much more).
'the french' becomes 'les' (les is the in french).
'without' is a deletion indicator.
'oomph' becomes 'it' (both can mean a special or striking quality).
'quite' with 'it' taken out is 'que'.
'bur'+'les'+'que'='BURLESQUE'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for burlesque that I've seen before include "Takeoff" , "Entertainment based on broad and earthy humour" , "Ludicrous satire" , "Parody - show with striptease?" , "Ludicrous imitation" .)