The USA never gains independence from the UK, and France, therefore unable to perform the Louisiana Purchase, claims Quebec.
Britain's and France's expansion
Of course, Britain and France expanded into other places, and rather than violence Britain recolonized "India" and Cherokee Nation was annexed by British North America. France expanded into Alaska and Greenland, while Britain expanded into the north part of what is now Mexico, which was not yet colonized by Spain.
Hawaii and Native Americans
Hawaii becomes Australian territory, and Native Americans were simply recolonized, later gaining independence.