Most people actually pronounce it closer to "pâ", which is the way the french settlers pronounced it. The loss of the sound "â" in France happened in the last century. Québec kept a few sounds that are now mostly lost in Europe. Also, some regions of France sometimes have the same pronunciation as Québec for these words. Look here : https://fr.wiktionary.org/wiki/pas#Prononciation , the "Hauts-de-France" recording is pretty much the same as in Québec. Not too surprising considering that most french settlers that went to America were from the north of France.

An other example of that, is the word "pâte" (pasta or paste, \pɑt\). Most french people pronounce it exactly the same way as "patte" (paw, \pat\). They lost the "ability" to pronounce the accent on the "â". But everyone still write it with the accent even if French people don't pronounce it, because that's the "old" way of saying it.
You can hear the difference here : https://fr.wiktionary.org/wiki/p%C3%A2te#Prononciation and here : https://fr.wiktionary.org/wiki/patte#Prononciation .