Firm agreement with Frenchman about cosmetics case (7)
I believe the answer is:
compact
'cosmetics case' is the definition.
(I've seen this before)
'firm agreement with frenchman' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'agreement' becomes 'pact' (a pact is an agreement or deal).
'with' means one lot of letters go next to another.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'pact' after 'm' is 'mpact'.
'co'+'mpact'='COMPACT'
'about' is the link.
(Other definitions for compact that I've seen before include "What comes initially with CD" , "Dense; agreement" , "Little" , "An official agreement" , "Tightly grouped" .)