King George really had absolutely nothing to do with the Treaty of Paris beyond ordering that it be a thing. That's what the monarchy does…when they're not wearing fancy-shmancy hats, giving speeches, or ordering a young Will Shakespeare to write a funny play in time for Twelfth Night.
When the Treaty of Paris was signed, he hadn't yet succumbed to the insanity that would earn him the unflattering nickname of "Mad King George." However, it's pretty probable that the treaty didn't help matters. This was the first time a New World colony had kicked out a European power. It was a humiliating defeat.
By 1788, he was officially the Mad King, a shell of his former self.