As an aside, Canada's joining the EU would likely help Canadian unity! Let's think about this for a moment. The EU has already established common education standards for many trades and professions,something Canadian provinces have so far failed to do. A union with the EU would likely expect Canadian provincial ministries of education to consult not only with other EU ministries of education to establish various educational standards for various trades and professions, but with other Canadian provicnes too, something successive federal governments have thus far failed to do, mainly owing to an archaic constitution.
After all, many EU constitutions are relatively new. The German, Spanish, Italian, and Greek ones stem from after WWII. The British one, though old, stems from a centralised monarchist and later imperialist system. This centralizatoin allowed the UK to be able to negotiate efficiently with other nations. France's is similar.
Canada's, on the other hand, was really an incremental step towards fusing separate British colonies into a new Dominion, an incremental step that has never been proceded by a second, except for the Charer of Rights and Freedoms, but that still never touched upon an archac division of responsibilities between governments.
A union with the EU would likely put pressure on Canadian Ministries of Education to start working together to establish common EU-wide standards and so, by implication, common Canadian standards too for various trades and professions, thus allowing for freer movement of labour not ony across the EU, but even between Canadian provinces.