Backing rich man with problem round old French house (7)
I believe the answer is:
bourbon
'old french house' is the definition.
(historical French royal house)
'backing rich man with problem round' is the wordplay.
I cannot really understand how this works, but
'man' could be 'bo' and 'bo' is present in the answer.
'round' could be 'o' (o is a circular letter) and 'o' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for bourbon that I've seen before include "Chocolate-flavoured biscuit" , "Rye whisky; biscuit" , "A drink" , "American whisky; biscuit" , "Rye whiskey" .)