We have the largest emission trading scheme in the world in the EU and it is actually working. The issue is that there are no taxes on international flights nor on kerosine. So flying is made artifically cheaper. That alone basicly would solve the problem.

The other big problem is that train tickets are not generally accepted across EU borders. That is a massive problem if one of your trains is delayed and you miss a connection due to that. You end up not being able to take an alternative train for free and do not get paid the normal fine from the train operator for long delays. There is some cooperation, so this is not the case for all international journeys, but still it is a problem.