In Europe there are actually five Ju 52's (four in Switzerland and one in Germany), DC-3's in Denmark, Norway, Sweden, Finland and Iceland (in addition to those in The Netherlands), and a Constellation in Switzerland, all carrying passengers. Additionally, Lufthansa is rebuilding a Constellation for passenger-carrying flights as well.
So it is evidently indeed possible.
If I recall correctly, there were some technical constraints imposed by EASA but the national authorities had some leeway in interpreting/dispensing with them, which however required applying for this, but Air Atlantique never entered into a corresponding dialogue with the CAA.