Crossword Genius

Rich food consumed in most of France, historically (6)

Ross

I believe the answer is:

gateau

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'rich food' is the definition.
(I've seen this before)

'consumed in most of france historically' is the wordplay.
I cannot quite understand how this works, but
'consumed' could be 'ate' (to eat is to consume food) and 'ate' is present in the answer.
The remaining letters 'gau' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for gateau that I've seen before include "(French?) cake" , "rich food" , "Gooey cake" , "Something French for 22?" , "Cream dessert cake" .)

I've seen this clue in The Independent.
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