Cheat demolished a posh French house (7)

I believe the answer is:

chateau

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'french house' is the definition.
'chateau' can be an answer for 'house' (chateau is a kind of house). I am not sure about the 'french' bit.

'cheat demolished a posh' is the wordplay.
'demolished' is an anagram indicator.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'cheat' with letters rearranged gives 'chate'.
'chate'+'a'+'u'='CHATEAU'

Can you help me to learn more?

(Other definitions for chateau that I've seen before include "Castle (1)" , "Impressive dwelling in France" , "French stately home" , "eg Margaux" , "Manor-house in France" .)

I've seen this clue in The Sun.

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