To the French, Paris say, has the right, cheerful readiness (8)
I believe the answer is:
alacrity
'cheerful readiness' is the definition.
'to the french paris say has the right' is the wordplay.
'to the french' becomes 'ala'.
'paris say' becomes 'city' (paris is a kind of city).
'has' means one lot of letters goes inside another.
'the right' becomes 'r' (common abbreviation).
'city' placed around 'r' is 'crity'.
'ala'+'crity'='ALACRITY'
(Other definitions for alacrity that I've seen before include "Prompt enthusiasm" , "'Briskness, promptness (8)'" , "Promptness, eagerness" , "Expedition" , "Brisk and cheerful readiness" .)