Oh, what a great question! I would say this would have happened in late 1776 after Washington lost New York to Gen Howe. At that time (with German mercenaries ready to rape and pillage New Jersey) 90% of the Americans wanted the war to end. Britain offered full pardons to everyone, offered American representation, and offered de facto independence. They even offered to make George Washington a Baron. Let's pretend the Continental Congress wisely took this deal, instead of following their ambitions. France would not have gone broke helping the Americans and fighting the British. There would have been no American Republic, no French Revolution, and no French Republic. No French Revolution means Napoleon would not become a general or, eventually, emperor. Venice and the Netherlands would have stayed republics. Spain would still possess the Louisiana Territory and the British-Americans would be in constant warfare with Spain to gain modern Florida, Alabama, and Mississippi. South and Central America would have never overthrown Spanish rule and would have remained colonies. With no Napoleon I, there would be no Napoleon III. The German and Italian principalities would never have unified; thus no WWI or WWII. With an interest in tobacco, sugar, and cotton, British investors would have delayed freeing their slaves for a few decades. And ending slavery probably would have meant a second attempt at American Revolution in the 1860s. I think a "Civil War" dealing with the slave question was unavoidable and would have happened due to the economic timeline.
The world was so drastically altered by the chain of events after the American Revolution that it's almost impossible to say what would have happened. World order would not have been as upset. I am certain of two things: 1) there would have been many more wars between the UK and Spain over the rest of North America. How France factored in is open to speculation. 2) Americans would have eventually fought another revolution against Britain to keep their slaves. Possibility of a world war of Britain against everyone--Netherlands, France, HRE, and Spain is likely.