Frenchman is in river: it's the end (6)
I believe the answer is:
demise
'the end' is the definition.
(demise is a kind of end)
'frenchman is in river' is the wordplay.
'frenchman' becomes 'M' (abbreviation for Monsieur).
'in' means one lot of letters goes inside another.
'river' becomes 'dee' (River Dee).
'm'+'is'='mis'
'mis' going inside 'dee' is 'DEMISE'.
'it's' acts as a link.
(Other definitions for demise that I've seen before include "Death, collapse" , "The end of something" , "Passing" , "Death or expiration" , "(Person's) death" .)