"God must be--no, God is--a Frenchman." -Marshal Louis-Gabriel Suchet
Spain, thanks to the prolonged effort against Britain, was desperately clinging to its colonies by 1810, trying to suck every bit of cash out of them it could. Finally, as per Napoleon's suggestion, they sold Florida to Georgia (which finally eased any tension on the borders between Florida, Georgia, and West Florida) for eight million Georgian Pounds plus a good amount of cotton, ammunition, firearms, and boots. It was a fair deal, but Spain needed more money to carry on. Thus, it began talks with France for the sale of the (already formerly French) Louisiana Territory.
This scared the living daylights out of the American countries, especially the Republican Union. Those countries might have been fine with Napoleon raising Hell in Europe, but the thought of Napoleon the Great in their own backyards was enough to cause insomnia. When France acquired Louisiana for 7,000,000 Francs, the Republican Union immediately raised an army and sent it to the Mississippi River to make sure Napoleon didn't get any big ideas about invading.
Napoleon, though, was not actually interested in invading the American republics. In fact, he liked most of them and saw no need to invade them whatsoever. Disunited, they weren't a threat. No, instead, he was eying British Canada, the ultimate prize over which the Seven Years' War was bloodily fought so many decades before. If he could take that back and end the humiliation which led ultimately led to the French Revolution, he would be a great leader indeed. He immediately drew up plans for a Kingdom of Quebec ruled by one of his officers or siblings, and the rest would likely become part of the French Empire proper. It was an impressive plan, but still would be extremely tough, if not outright impossible, to pull off with the Royal Navy causing problems.
That, concluded Napoleon, was the moment his greatest brainchild was born. He suddenly realized that if he announced a total partition of the faltering British Empire, from India to Jamaica, other countries would likely love to get in on the profitable venture regardless of how much they hated his guts. Napoleon was top dog in the European neighborhood, and Britain was now the scrawny, malnourished whelp getting the snot beaten out of it on the regular. It was always better to be on the top dog's side than the scrawny whelp's regardless if the scrawny whelp was formerly your best friend.
So, Russia was told that if the Imperial Russian Fleet helped rip through the Royal Navy, it would get to keep not only Alaska and the surrounding area, but would have part of the North American west coast blocked off for its exclusive ownership. The Czar, Alexander, without having any idea what the offered territory was like, thought this was great, of course, and an English historian later claimed that "Alexander was willing to sell his soul to the devil for a bit of beachfront property in Eskimoland." He was also plied with very lucrative trade deals which helped soften the blow when he realized later most of the land in America was useless.
When the offer was sent to King Friedrich Wilhelm III promising African and South American territory in exchange for providing infantry and supplies for the invasion of Canada, the Prussian monarch reluctantly accepted, mostly because the French Imperial Army had several of its German regiments in his capital to enforce the Continental System and depose him if he tried anything
Similar requests were sent to all the major countries in France's sphere. As for minor countries; they either were of no real possible use or would just follow along out of fear without actually even being promised anything as reward.
Thus, the plans for the Canadian Invasion were completed by early 1811. In the spring of 1812, the fleets were to do battle with the Royal Navy in a sea battle for the ages.
Or at least, that was what was supposed to happen.
British spies knew had found out about the Canadian Plot as early as just several weeks after the proposal was sent to Czar Alexander. William had to do something. Anything. He would not allow Britain to lose Canada.
Wills raised a massive army, pushing the Royal economy even deeper into the darkest pits of the metaphorical outhouse. Thousands of men were shipped to Canada. Thousands of men in Canada itself were formed into militias. William had no way of paying for all this, so he had to believe he would win and keep Canada, and then use the momentum to possibly raid the French coast and perhaps invade Denmark or Greece or some other such place, and then slowly strike back against the Empire. If he did that, chances were Austria would side with him again, and then Prussia. With any luck, Austria, Prussia, Sweden, and perhaps one or two other former allies would return to his side and defeat the Franco-Spanish-Russian menace in a possible War of the Sixth Coalition.
The truth is that it probably would have happened. Invading Canada would be like invading Russia. The freezing temperatures, vast open plains, rugged mountains, and relatively low population made it desirable in the past for sake of furs and colonial bragging rights, but it was not a good target for Napoleon. Russia would probably "claim" western Canada anyway, and Britain would likely do nothing in response. It was vast emptiness.
Up-and-coming Arthur Wellesley, thought the plan smelled of "French froggery," and was the only one to voice this opinion to the King, but William was too panicked to listen. The stress was starting to get to him, and he was showing signs of mental illness just like the two Georges before him. He became obsessive over protecting Canada, and it was the biggest mistake he ever made.