Zoogster - The Brits couldn't have come up with the technology in the 1700's to make AK-47's, or, like you say, they would have had them. Plain and simple.
"Coming up with" and copying and applying the new technology are very different things.
Just an example of a round of ammunition from a battlefield would have put the world many steps ahead.
The leap from cartridge ammunition to repeating arms is not very far apart.
Full-auto was invented before semi-auto.
I have little doubt that they could build new firearms based on the AK if they had an example.
Watchmakers alone, the mechanical engineers of the time, most certainly could have understood the mechanical process and copied or made every single component of an AK except the barrel.
Or entirely new weapons that utilized the same or a similar mechanical process.
The Industrial Revolution was just underway, and it would be centered in England, more than anywhere else in the world.
Something compact like small arms that delivered much greater firepower, would have benefited the British more than anyone. A people that ruled the sea, and could have transported such compact arms all over the world far easier than larger support weapons.
There was many traitors on both sides (one of the most famous being General Benedict Arnold of the Continental Army), so in addition to seized arms on the battlefield, you would have had examples of any tech held by one side given to the other side.
The Continental Army was having a horrible time just keeping itself equipped with technology they already had, and keeping what they had in working condition.
Men were walking in the snow with rags on their feet.
New technology would have benefited the British far more, and been manufactured more quickly by the British.
Interestingly enough after the war the primary trading partner that kept the American colonies afloat was the British!
Many of the French who helped the colonists didn't really care a lot about them, but rather were working to divide and conquer their enemy, the British.
To this end they helped the Colonies a great deal, but it was only to weaken their enemy, whose economy depended a great deal on trade with places like America and taxes generated.
The French had great animosity for the colonists, people they just fought a decade before in one of the most bloody global conflicts in the world up to that point, the Seven Years War (French and Indian War on American soil.)
Had their enemy the British actually been soundly defeated, and maybe even invaded at home and conquered, the French would have soon turned on the American colonies.
Things like the Louisiana Purchase would have probably never happened (France sold it because of major conflicts at home at the time, conflicts with the British, and in order to increase the power of an enemy of the British.)
"This accession of territory affirms forever the power of the United States, and I have given England a maritime rival who sooner or later will humble her pride." -Napoleon Bonaparte
Without the Louisiana Purchase, the American colonies would have not likely reached west of them either, to claim the additional land from the Rockies to the West Coast, or South from Texas to California.
Leaving the American Colonies a small entity on the East Coast.
So the United States would have probably never become what it has if it had actually squashed the British, rather than just beating them back.
France would have likely set her eyes back on the American Mainland able to devote a lot more attention to the New World without a British enemy, and the hostilities of the French and Indian War continued.