That's a bit of a myth. The dialects have been evolving separately since that time; you can't say either is closer to the branch point than the other.

The reason French people believe this is because yes, there is some old vocabulary like souliers retained in Quebec, but on the other hand there are also some features that they've lost over time that are retained in France, like using si instead of oui to contradict a negative.

Sure they do, but usually it is only a few weeks of adaptation. The differences are well documented, look them up! It's still the same language.