I would suggest transfer of a good portion to North American zoos.
Invasive species they are not quite frankly, I have not heard of large scale deliberate or accidental releases,. The Canadian beaver is an invasive in southernmost Fireland Chile-Argentina where they are damaging the tree line and submerging habitats.
Dewas et al (2012), to asses the beaver populations in France, reviewed the occurrence of
C. canadensis in western Europe, and they list introductions in Switzerland, Poland and France which likely have been eradicated or died out by know. However, they also note that
C. canadensis was found in beaver populations in Belgium, Luxembourg and Germany - and at least 19 individuals were caught, at least six of which were released again after sterilization. To fully support further recolonisation of beaver in Europe, it remains important to be vigilant about
C. canadensis popping up, especially as the source of the recently caught beavers is not fully understood (e.g. there is a possibility that
C. canadensis were among the source populations used for reintroduction).
Whether you can call that invasive or not is a matter of opinion, but Canadian beaver can certainly survive and reproduce in the wild in Europe and thereby complicate beaver conservation here. Given that Canadian beavers are not particularly popular zoo animals, there is no conservation value in keeping them here, and the European species is extremely similar to it's North American counterpart, I'm all for phasing out the species. However, with an eye on animal welfare, I think it would be better to sterilize all remaining animals and just let them live out their lives here.
Reference:
Dewas, M., Herr, J., Schley, L., Angst, C., Manet, B., Landry, P., & Catusse, M. (2012). Recovery and status of native and introduced beavers Castor fiber and Castor canadensis in France and neighbouring countries.
Mammal Review,
42(2), 144-165.