Canadian political and legal institutions are also modelled on European precedents, and more than half of Canadians identify as European in ancestry.

There could also be some perks for both sides to a closer union. As Pignal suggests, Canada could offer the EU access to vast reserves of strategic resources much rarer on the continent, like rare earth minerals and fossil fuels.

Canada, meanwhile, might benefit from access to Europe's large and skilled labour market — and reduce its dependence on the U.S. and its volatile politics.

"Ottawa must prepare for a world where Washington is less reliable," said Teona Lavrelashvili, a visiting fellow at the Martens Centre, an EU think-tank in Brussels. "Strengthening engagement with Europe … is not just strategic, but essential."