It is obvious that the american colonies wanted to rule themselves and not pay taxes to Britain, but I also read that it was seen as a major betrayal to the British and allowed the French to even make plans to invade Britain, effectively reducing the number of troops deployed to America.
Also, to what extent did this balance of power shift allow Napoleon to conquer much of Europe during his reign in the years to come?
There was a good description of French assistance to the Continental Army here, by u/Takeoffdpantsnjaket
. It's hard to overstate the importance of France. Not just the enormous amounts of arms and supplies, but the crucial blockade of Cornwallis' forces at Yorktown by the French fleet. You will sometimes encounter counterfactual arguments that suggest eventually George Washington would have tired out the British and won, anyway. And it is true that he had managed to keep an army in the field with very meager supplies in the early stage of the Seven Years War. But considering the huge size of the French investments, it's hard to imagine how the colonists could have made up the difference themselves. They really didn't have the means to manufacture anywhere near enough of the materiél needed to fight a war.
Can't say what effect the Revolutionary War had on Napoleon's chances- though, of course, if the Old Regime hadn't foundered on paying for that war, there likely would not have been the French Revolution that gave Napoleon his opportunity.
Just to piggy back off the last comment, it is important to view the events of France entering the American revolution in a larger context. France joining the war did not mean that they would only fight in the American colonies. This can truly be considered the First World War. France and Britain each had colonies throughout the world at this time. Being at war with France meant that Britain had other, vital, colonies that were immune to American invasion now threatened by the French and in need of protection. This is specifically evident in admiral de grasse “feinting” towards the sugar islands in the Caribbean which drew significant British strength away from the American colonies, allowing for his return to blockade Yorktown. The last battle of this world war was fought in India, far from American shores, by the same Cornwallis that was defeated at Yorktown.
In regards to Napoleon I have yet to see conclusive evidence that the American revolution disrupted the balance of power in Europe. Britain, aside from losing the American colonies, can be considered the victor on the world wide stage vs France, gaining territory in, for example, India. More importantly, trade with the American colonies actually INCREASED after the war, specifically in the agricultural sectors. This fact was paramount in the about face British governments had towards future colonies and their independence. Before it was thought that to lose the colony meant to lose trade and therefore money, which was proved not to be the case.
I still remember my history teacher giving us this analogy:
“Saying that the United States successfully defeated the British, with some help from France, is akin to an eight year old boy coming home from hunting to tell his mother that “Daddy and I shot the bear!” We all know who tracked the animal, carried the rifle, aimed, and pulled the trigger boy; but you go ahead and keep telling yourself you did it, “with some help from Daddy.” 😜