One Frenchman, out-of-date, reaches stalemate (7)
I believe the answer is:
impasse
'stalemate' is the definition.
(I know that stalemate can be written as impasse)
'one frenchman out-of-date' is the wordplay.
'one' becomes 'i' (Roman numeral).
'frenchman' becomes 'm' (abbreviation for Monsieur).
'out-of-date' becomes 'passe' (synonyms).
'i'+'m'+'passe'='IMPASSE'
'reaches' acts as a link.
(Other definitions for impasse that I've seen before include "hopeless difficulty" , "cul-de-sac" , "Stalling of negotiations" , "Lack of movement" , "Stalemate situation" .)