A lot of quality in military canteen - Frenchman’s unusual influence (9)

I believe the answer is:

mesmerism

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'unusual influence' is the definition.
'mesmerism' can be an answer for 'influence' (mesmerism is a kind of influence). I am not sure about the 'unusual' bit.

'a lot of quality in military canteen frenchman's' is the wordplay.
'a lot of quality' becomes 'meri' (I am not sure about this - if you are sure you should believe this answer much more).
'in' means one lot of letters goes inside another.
'military canteen' becomes 'mess' (I've seen this before).
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'meri' put within 'mess' is 'mesmeris'.
'mesmeris'+'m'='MESMERISM'

Can you help me to learn more?

I've seen this clue in The Independent.

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