A deeply interesting concept. However, first of all:
Orangebird763 wrote:
And regarding the Anglo-Saxons, yes, this leads to the English language being developed in Normandy, Brittany, Guernsey, and Jersey; as Napoleonic France collapsed and territories declared independence, English-speaking Guernsey and Jersey declare independence (from France, as there is no British Crown for them to fall within). I'm not sure if this event is all too plausible though, as I have little experience with European history.
I really don't believe that a Napoleonic France could really exist in your timeline as I think history would erase that event. A Napoleonic character could definitely arise but not necessarily from France.
As discussed previously, the Romans would be stronger. Another impact would be the Vikings would never know of lands to their west. This might push their incursions into Europe into the future by another decade or so. Another thing you could perhaps play around with could be that temperatures in the north such as around Iceland and Greenland remain as warm as they were before the mini ice age, perhaps as a butterfly effect (chalk it up to a larger body of water generating more moisture or something thus keeping the region warm). This could directly impact the Norse and could mean that perhaps their Vinland colony could survive.
About North America, the continent would be drastically reshaped. The British had a large impact on the continent, and their 13 colonies that became the US were responsible for removing many other colonies from the continent. The Spanish would probably not be able to colonise up to Virginia as French Loiusiana would probably also be around. The Dutch were also at the eastern seaboard before the Brits kicked them out, so perhaps without the British the Dutch could potentially hold onto the foothold and expand in the region - most likely coming into conflict with French Quebec and Louisiana. I could see the French Louisiana being pressured at one side by the Spanish and the other by the Dutch (who would probably want as much control over the Great Lakes as they could get for trading purposes). Russia was also involved in North America, and if the Spanish are more focused toward their east with the French then the Russians would easily be able to take large swathes of land in OTL Canada. Perhaps they could get lucky and end up something like this (but with more lands in Canada to call their own). And if Vinland survives, then North America could really be an interesting place.
Possibly the biggest gainers from the lack of Britian in terms of colonies could actually be the Dutch, who had established many small colonies before the Brits got stronger.