Crossword Genius

Director from Left Bank originally visiting this French river that's inundated factory (5,1,7)

Ross

I believe the answer is:

cecil b demille

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'director from left bank originally visiting' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'this french river that's inundated factory' is the wordplay.
I cannot really see how this works, but
'factory' could be 'mill' (mill is a type of factory) and 'mill' is found in the answer.
'river' could be 'dee' (River Dee) and 'dee' is located in the remaining letters.
'this french' could be 'ce' (I've seen this in other clues) and 'ce' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Times.
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