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' (abbreviation for company).
'agreement' becomes 'pact' (a pact is an agreement or deal).
'with' says to put letters next to each other.
'frenchman' becomes 'm' (abbreviation for Monsieur).
'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" .)