Nope, NAFTA was written as a 'trade agreement', rather than a treaty, and only needed 50% + 1 votes in both houses to pass. It passed in the Senate with 61 votes and in the House 234-200. A treaty requires 2/3 agreement in the Senate.
The United States should not copy Europe with a North American Union (they can copy the United States with a United States of Europe). Also, the country with Canada and Mexico should still be the United States of America. The country stayed the United States of America after the Louisiana Purchase, Gadsen Purchase, Mexican American War, taking over some of Oregon Country, Alaska, Hawaii, taking over some parts of Maine, etc.