The Third Kingdom of Burgundy has problems early on with the Church, there were many in the Church who did not want to see France split. The Holy Roman Empire was also a thorn in its side. Luckily none of the skirmishes between the two became an all-out war. The support of the English became important in such affairs, and this dependence did not please many in Burgundy.
When the 'New World' was discovered Spain and Portugal quickly moved to exploit South America. A diminished France would join them in the south. England and Burgundy became the dominate European powers in North America a century later.
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Sean Sherman has been a fan of alternate timelines ever since seeing Spock with a goatee. By day he is a CPA, at night he explores the multiverse and shares his findings over at his blog, Other Times.