A French water supply is not healthy (6)

I believe the answer is:

unwell

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'is not healthy' is the definition.
I can't tell whether this definition defines the answer.

'a french water' is the wordplay.
'a french' becomes 'un' ('a' in French).
'water' becomes 'well' (well water is a kind of water).
'un'+'well'='UNWELL'

'supply' acts as a link.

Can you help me to learn more?

(Other definitions for unwell that I've seen before include "Ill, not in good health" , "Sickly, low" , "Indisposed" , "Poorly" , "funny" .)

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