The Treaty of Paris was an agreement between King George and the United States of America, not 13 seperate, sovereign entities. It was proclaimed between the U.S. and Great Britain and was signed by John Adams, Ben Franklin, and John Jay on behalf of the U.S.
Indeed it was and you should take note of the FACT that not one person on either side objected to the fact that each and every one of the thirteen former colonies was singularly named and referred to as free, sovereign, and independent states in that document!