IMDB says

Alouette
(uncredited)
Traditional French folksong
Sung to accompaniment of accordion by Laurence Olivier

But that's definitely not the song in question.

Film composer Ralph Vaughan Williams wrote the score for this movie and included titles were:

Prelude [opening titles] (2:13)
Prologue (11:20)
Control Room Alert (2:03)
Hudson Bay Post (1:27)
Looting the Store (0:46)
Death of Kühnecke (1:57)
Hutterite Settlement (a) Anna's Volkslied (3:14)
Hutterite Settlement (b) The Wheat Harvest (1:47)
Winnipeg I (2:50)
Winnipeg II (1:08)
Nazi March (3:15)
Indian Music I (0:29)
Indian Music II (1:00)
Indian Music III (0:46)
Nazis on the run & The Lake in the Mountains (2:08)
Prelude [closing titles] (2:12)

I don't think any of those are right either. You'll need someone who understands French to track it down. I'm no good at trying to guess which letters they decide to leave out or not when pronouncing a word