Country seat's opening for girl (7)

I believe the answer is:

frances

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'girl' is the definition.

'country seat's opening' is the wordplay.
'country' becomes 'france' (France is an example).
'seat's opening' becomes 's' (I can't justify this - if you can you should believe this answer much more).
'france'+'s'='FRANCES'

'for' is the link.

Can you help me to learn more?

(Other definitions for frances that I've seen before include "Name" , "Girl" .)

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