A French, extremely hairy soldier leads exercise, noting infantrymen's clothes as not clean (10)

I believe the answer is:

unhygienic

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'exercise noting infantrymen's clothes as not clean' is the definition.
I can't judge whether this definition defines the answer.

'a french extremely hairy soldier leads' is the wordplay.
'a french' becomes 'un' ('a' in French).
'extremely' suggests removing the centre (only the extremes of the word are used).
'soldier' becomes 'GI' (term for US soldier).
'leads' becomes 'enic' (I can't explain this - if you can you should believe this answer much more).
'hairy' with its centre removed is 'hy'.
'un'+'hy'+'gi'+'enic'='UNHYGIENIC'

Can you help me to learn more?

(Other definitions for unhygienic that I've seen before include "Dirty" , "Unsanitary" .)

I've seen this clue in The Irish Times.

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