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I once encountered a theory that North American english was potentially closer to historical english because it was less influenced by neighboring countries. I doubt that, now. But it's an interesting idea.
North American French is like that
It is much more formal and traditional compared to France French (No idea about Haiti)
Because of laws preventing loan words
Québec French is a lot of things, but I wouldn't call it formal. Heck, one of the core formal things about French (vouvoiement) barely gets used here in Canada, compared to France/Belgium/Switzerland where it's omnipresent.
Regarding the traditional aspects, I'd say it preserves a certain tradition, but it's also full of innovations. It's far from medieval! I wouldn't say French-speakers in Quebec speak like kings and queens of the 1700s.
It is very different to European or African French, that's for sure!
https://theinternetsaysitstrue.com/2022/08/08/is-the-original-english-accent-still-alive-in-parts-of-the-united-states/ an interesting article on the subject that includes videos
As a yank who lived in the UK (East Sussex) for several years, I can share the sentiments of my mates there that they believe we Americans still speak a more traditional version of the language than they do now. Specifically pronunciation of words.
For example, Americans have retained the pronunciation of the final “r” in words like “father” and “mother,” while the UK has dropped it. Americans have maintained the “flat a” sound of cat in words like “path” and “class” whereas the UK has mostly replaced that sound with the “broad a” of “father.”
It's not an exact science, but the rate of change in the language there has gone beyond the 18th century version we Americans still speak today and thus, it can be said American English, at least pronunciation, is more traditional.
On the class/path a: it depends where you are in the UK. In the north, it tends to be the flat a, in the south it tends to be the broad a. There's a lot of variation in accent within the UK, to the point that you can identify pretty accurately where someone is from using something this quiz: https://www.nytimes.com/interactive/2019/02/15/upshot/british-irish-dialect-quiz.html.
Anecdotally, I think it is becoming a bit more uniform than it used to be, due to people moving around more than they did historically, though
Then there's the people who say Shakespeare makes much more sense, flows better, and better play on words when spoken with an older UK accent (or Irish?), so nothing like North American.
(Lots of search results but no easy blurb to read on what it was. But I recall hearing some and it was nothing like North American accent.)
To bea or not to bea ... https://www.youtube.com/watch?v=qYiYd9RcK5M