Speaking as someone who knows what we have lost by leaving: the benefits are more than just economic and more than just trade. There are things that some in Canada would balk at - the EU budget and how it decides to prioritise spending could be an issue.
Basically, member countries either put money into a pot or receive and it's then hopefully dished out to help develop the poorer regions of Europe as well as protect certain communities. You also get the benefit of collective bargaining when it comes to dealing with giants like China, the USA, India etc as well as some of the mega-corporations. Little Luxembourg could never hold Apple or Google to account and force them to comply with common power chargers (one example) or force them to delete old data (another example.)
You also get free travel, common worker's rights and healthcare - so if you travel to work in one country and become unwell for example, the same right to free healthcare is given as to natural citizens. If yu wanted to go to work in another EU nation, you could (subject to proving that you weren't going to drain the new host nation resources)
Your universities, colleges and schools could take part in the Erasmus or Leonardo programs and you would have Canadian students allowed to travel to study for up to a year in another nation or have exchange visits of varying length and there would be reciprocal agreements for other EU students.
Sovereignty was a largely falsehood that Brexit used to sell the leave campaign. The only thing you couldn't do as a member was strike a free trade deal with say China or the USA and then become a back door into the EU for goods that would otherwise be banned. On the other hand, as a small member like Luxembourg again - you could sit at the same table as China and have 26 other nations with you in armwrestling the Chinese dealers. On sovereignty, if France wanted to start a war with Mongolia - nothing in the EU rules prevents that. There's a lot more like that within the foundations of the EU.
New members also have to agree to swap currency to the euro; however if Canada was actually part of the European continent and wanted to join - I'm pretty sure a delay could be agreed, and with no end date to the agreement.
Other things that would hit would be environment laws, "no" to the death penalty, but you could also join several scientific groups to mutually develop new technologies.
The EU does demand that membership is based on being a European nation but that didn't stop Turkey / Georgia and other near-Asian nations like Armenia seeking to join.
Find out how enlargement works and how countries can join the European Union.
www.europarl.europa.eu
Personally, I think they won't let muslim nations join - certainly France and a couple of others blocked Turkey's bid several times while other nations like Poland / Slovakia etc did not have a 40 year wait and still unable to join.
I'd defer to
@PeteEU here but as I see it there are three levels of trade deal
Full EU member's entitlements - no barriers to goods and services, common standards and free movement of people.
European Free Trade Area - with members like Norway, Switzerland etc who have to follow EU trade practices but can strike their own deals with 3rd parties. You have no say over the creation of rules and processes as that is for member nations alone.
Free Trade Agreements - such as the EU has with Canada, China etc. Goods and services within agreed areas have most if not all trade barriers removed.