Jordan Peterson and Catholicism

Dr Peterson would possibly correct you and say "Old North America" (at least the English-speaking part), as he is Canadian.  WRT traditional family values, Canada and the US were probably far more similar than different.  Canadians typically say "North America" as a way to speak of the US and Canada (sans Québec) as a single culture and economy; it's fairly uncommon for a USAmerican to use the term "North America" that way.

If the British had won the Revolutionary War, Canada and the US would likely be a single country from the Arctic Circle to (arguably) the Rio Grande, possibly called British North America or Columbia; like Australia or New Zealand, they'd have to call it something.  That would be one amazing and very powerful country (and likely Québec would have retained its distinct culture, legal system, and so on, just as it does now).

He's politically incorrect and invites a wide range of opinions on his writings, but he is one of the few relatively famous public intellectuals in North America.  Unlike France, this isn't a culture that fosters or deeply appreciates public intellectuals.  We're too busy slobbering all over Taylor Swift and the Kardashians.  (But to give Kim her due, her father was a prominent attorney, and she is studying to be an attorney herself, albeit in a nontraditional program that provides a route to the California bar exam.  She's far from being an airhead.  More importantly, God bless her, she was baptized a few years ago into the Armenian Apostolic Church, and is arguably the most well-known Orthodox Christian in the United States.)