Trains are also more expensive to run than planes because they need more infrastructure to operate, and that infrastructure is high maintenance. So we have almost no competition, high operating costs, and we've set it up so the people operating the trains are in opposition to each other and have no incentive or obligation to work together to lower prices or improve the service.
Nationalise it. All of it. And let's just accept that there are some things that simply shouldn't be run by the private sector.
And I realise that "Nationalisation" in the context of the EU is the wrong word. What I'm saying is the that EU should run the whole thing. Whatever that's called... Federalisation? I don't know.