The film was "The Trap" (1966)

This is from the "trivia" section of IMDb's information about "The Trap."

The piece of music used as Oliver Reed canoes down river (also called "The Trap") is now used by UK broadcaster The BBC for its coverage of The London Marathon.

And this is from a user review:

The folk song version of the Ron Goodwin's theme, as sung song by beardy french canadian trapper (Oliver Reed) is a classic, (...'When I'm a man I'll take me a wife, and live in a house on a hill, a hill...and she shall have diamonds & pearls, and pearls, and she shall have diamonds and pearls!') and is now used every year as the music for The London Marathon.