Much more likely is looser employment visas and maybe allowing Canadians have an easier time moving for things like retirement, etc. I'm not holding my breath, though.
What you're thinking about is the "single market" - which, even if the name could deceive, also applies to people, including the right to go work anywhere within the single market for citizens of single market countries. Which is what many brits always hated, as they wanted single market for services and goods, but not for people.
Single market doesn't imply Schengen though - eg I as an EU citizen have the right to move to Ireland for work, but I still need to go through border checks as Ireland is outside of Schengen (because they have free movement with NI).