This is sort of a comment but it has outgrown in length the comment box. For the question directly: we do not know, it depends on which airline are you flying -- however, you can deduce that from the airport where you are transferring. Here's how.
A US carrier carrying passengers from Canada to the European Union directly would be a Seventh Freedom flight (list of freedoms)
the right or privilege, in respect of scheduled international air services, granted by one State to another State, of transporting traffic between the territory of the granting State and any third State with no requirement to include on such operation any point in the territory of the recipient State, i.e the service need not connect to or be an extension of any service to/from the home State of the carrier.
ICAO characterizes all "freedoms" beyond the Fifth as "so-called" because only the first five "freedoms" have been officially recognized as such by international treaty.
In short, no such thing exists. A Canada-EU nonstop flight can only be operated by
- A Canadian airline
- An EU airline
- Another airline coming from or going to their home state, using Canada or EU as a stopover, a so called Fifth Freedom Flight. These are are rare especially in Canada: Cathay used to do a Hong Kong - Vancouver - New York (1996-2020, it was stopped independently of covid, it was losing money) and right now I believe the only one is the Beijing-Montreal-Havana flight by Air China. So to the best of my knowledge, there's none with a Canada-EU leg. There are a few Fifth Freedom flights with US-EU legs both in the (home airport)-US-EU and in the US-EU-(home airport) configuration but nothing with Canada.
In theory, a US carrier could do a Fifth Freedom flight but typically such flights exist because the home airport is very far away like Singapore or Cook Islands and are pretty much forced to land inbetween. A relatively recent (pre-covid) list can be found here.
And all this matters because now we now know the transfer airport is home state for the carrier as it doesn't have (or use) the freedoms to do otherwise. If it's a US airport then it's a US airline and you can check Wikipedia which airline has a hub there to figure it out, like Dallas is AA, Minneapolis is Delta and Houston / Chicago / Newark is United (luckily enough there are no direct flights to JFK which is both a DL and an AA hub). If it's an EU airport then the operating carrier must be either a Canadian or an EU airline (Air Canada, Westjet and Air Transat are Canadian so they are always a possibility, Amsterdam can be KLM, Frankfurt can be Lufthansa, Paris can be Air France, London can be British Airways).
Stealing an infographics from https://transportgeography.org/contents/chapter5/air-transport/air-freedom-rights/ (first is airspace transit, second is technical stop, the rest are self explanatory)