Spin-off from the excellent On the Naming of Canada Thread.
The natives that Cartier encountered in Gaspé Bay were St. Lawrence Iroquoians. If this video was 100% accurate, the aboriginals would be speaking that language. I really doubt this is case because it went extinct just a few decades after the encounter and the only attestations of it that we have are two short vocabulary lists.
So, I guess that what we hear in the video is another Iroquoian language but which one is it ?
Mohawk or Huron-Wyandot are possible and sort of acceptable stand-ins as they were spoken in areas directly adjacent to the St. Lawrence Iroquoians’ lands and still have native speakers nowadays, although not in their original area as far as Huron-Wyandot is concerned.