Borders outside close to free French city (5)

I believe the answer is:

reims

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'french city' is the definition.
(city in France)

'borders outside close to' is the wordplay.
'borders' becomes 'rims' (rim can mean an edge or border).
'outside' is an insertion indicator (some letters go outside others).
'close to' becomes 'e' (I can't justify this - if you can you should believe this answer much more).
'rims' enclosing 'e' is 'REIMS'.

'free' acts as a link.
This may not be right. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for reims that I've seen before include "City of northeast France" , "City, the traditional site for crowning French kings" , "city in NE France" , "Champagne capital (variant spelling)" .)

I've seen this clue in The Times.

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