A lean-to the Frenchman built (7)

I believe the answer is:

anatole

I'm a little stuck... Click here to teach me more about this clue!

'frenchman built' is the definition.
I can't tell whether this defines the answer.

'a lean-to' is the wordplay.
'a lean-to' can be anagrammed to 'ANATOLE'.
But, I'm not sure how this is indicated.

'the' is the link.

Can you help me to learn more?

(Other definitions for anatole that I've seen before include "France maybe" , "- - France, French novelist" , "France perhaps" , "France possibly" , "- France, Fr. writer" .)

I've seen this clue in the Evening Standard.

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