The French king catches chill (5)
I believe the answer is:
relax
'chill' is the definition.
(chill can mean to relax)
'the french king catches' is the wordplay.
'the french' becomes 'la' (one of the French words for 'the').
'king' becomes 'rex' ('king' in Latin).
'catches' means one lot of letters goes inside another.
'la' placed within 'rex' is 'RELAX'.
(Other definitions for relax that I've seen before include "Take one's ease" , "Hang loose" , "Chill out" , "Loosen up, slow down" , "Take it easy, don't be so tense" .)