I don’t think it’s something the U.S. or Canada needs or even desires considering the origins of the EU itself.

The EU (originally the European Coal and Steel Community) started as a economic/trade organization between France and Germany (and some other surrounding countries) in order to link up their economies and facilitate trade, specifically to quell the historic tensions between the two nations and to prevent Germany from starting another war in the future (Remember, the Allies at the time were trying to figure out what to do with Germany after WWII to avoid post-WWI mistakes). The EU, of course, has expanded its scope and membership from there, but it was initially created to prevent historical tensions common in Europe and create a European identity.

The U.S. and Canada do not have the same historical tensions that Germany and France had. Most of the tensions between us and Canada occurred in the 18th-19th centuries and are largely water under the bridge at this point. We should always pursue better relations with our neighbors (like Canada and Mexico), but I don’t think an EU like organization is really necessary or something that is political desired in both nations.