One's dropped into the French river — here's rest! (7)
I believe the answer is:
leisure
'rest' is the definition.
(leisure is a kind of rest)
'one's dropped into the french river' is the wordplay.
'one's' becomes 'is' (Roman numeral).
'dropped into' indicates putting letters inside.
'the french' becomes 'le'.
'river' becomes 'ure' (I have seen 'River of Wensleydale ' mean 'ure' so perhaps 'river' could also mean 'ure'**).
'le'+'ure'='leure'
'is' going into 'leure' is 'LEISURE'.
'here's' is the link.
(Other definitions for leisure that I've seen before include "Free time as for resting or play" , "Freedom from work" , "Time for relaxing" , "Use lire (anag)" , "retirement" .)