It all depends on what time period you are talking about, but if you go back to 1900 or earlier there was not a single "Anglo mass", and in fact many of the people with ancestors from the British Isles did not speak English. A large percentage (as in, majorities in many areas) of rural Scottish immigrants spoke Gaelic. If you go back to the 18th century, many immigrants from England didn't speak English either. There were more linguistic minority groups then (both in England and France -- Wikipedia cites an estimate that over 39% of France's population in 1860 spoke Occitan! http://en.wikipedia.org/wiki/Vergonha
) and they were disproportionately likely to emigrate from their home countries. There weren't a lot of affluent Londoners or Parisians making the crossing back in 1650 or 1750.
In Western Canada many of the original settlers were from Germany or Eastern Europe.
Today the question of "ethnic origin" doesn't even make sense for a lot of people. For a certain part of the population the "French vs. English" distinction is also pretty murky.