John Quincy Adams spent a large fraction of his childhood and adolescence in Europe. He went with his father to Europe when he was negotiating the independence of the U.S.
He kept an amazing diary, which covered his travels and work for the US government, including the Treaty.
He’s obviously a smart guy, but he was 16 only years old when the Treaty of Paris was signed, so it’s hard to gauge how much he grasped of what was going on around him. He’s got an entry noting “3. Signature of the Definitive Treaty”, but it’s also preceded by “2. Dined at Auteuil. French Comedy: Le joueur & le retour imprévu” and “4. Dined at Mr. Hartley’s”