It would be interesting to run a program that considers some of the possible outcomes if the colonists hadn't rebelled and won. Would many of the monarchies change to some form of Democracy or would they stay on course and maintain their control over people?
The possible course of world history without a USA is an intriguing question. At the time of the American Revolution, Great Britain had an elected parliament. Granted, only male land-owners could vote, but it was progress.
By the late 19th century, Imperial Germany was roughly equally democratic to Great Britain - more so in some respects, less so in others. In other words, monarchy does not necessarily mean autocracy.
Would the Kaiser have abdicated/Weimar Republic come to be?
Without the 1st World War, this wasn't going to happen. It's difficult to say whether that war would have started if there were no USA. There are a lot of moving parts to world affairs.
Would Britain have attacked North America in the event that France had become the controlling power here? I think they would, because the original colonies were not only a way for people to leave England, but England used them as a business venture and a source for many raw materials.
Well, France already controlled far more North American territory than Great Britain at the beginning of the 7-Years War. That said, the population of the British colonies far, far exceeded that of the French and was concentrated in a smaller geographical area. I doubt the French would have been able to overwhelm them, regardless of the outcome of the wider war. And, the British did not fight with the French over North America for its own sake. It was just a consequence of the wider war - the 7-Years war has been called the
real 1st World War.
