Exactly like personality, a Frenchman in London area (8)

I believe the answer is:

selfsame

I'm a little stuck... Click here to teach me more about this clue!

'exactly like' is the definition.
'selfsame' can be an answer for 'like' (thesaurus). I am unsure of the 'exactly' bit.

'personality a frenchman in london area' is the wordplay.
'personality' becomes 'self' (I've seen this in another clue).
'frenchman' becomes 'M' (abbreviation for Monsieur).
'in' indicates putting letters inside.
'london area' becomes 'SE' (postcode for south east London).
'a'+'m'='am'
'am' going within 'se' is 'same'.
'self'+'same'='SELFSAME'

Can you help me to learn more?

(Other definitions for selfsame that I've seen before include "The identical kind, not changed or different" , "Exactly identical" .)

I've seen this clue in The Telegraph.

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