What would have happened in the years following the war if the American revolutionists had lost the Battle of Saratoga and not gained French support?
If the colonists had not won the Battle of Saratoga and, with it, French support, they would almost certainly not have won the war. Therefore, the years after the war would presumably have seen the colonies continuing to be ruled by Britain. This rule might well have been harsher than it had been before the Revolution.
French assistance was vital to the US cause. The French gave men and materiel and also provided very timely naval support that (among other things) allowed the colonists to win the Battle of Yorktown. If this support had not been given, the colonists would likely have lost the war.
If the colonists lost, the British would probably have cracked down on the colonies, at least in the short term. If they had, the years after the war would likely have been fairly oppressive for the colonists. They would likely have lost their ability to govern themselves in any significant way. Taxes and regulation might well have increased. In short, the post-war years would surely have been a very dark time for the colonies.