One of the main reasons for the disparity is the lower taxes that the aviation industry benefits from.
If you fly from Paris to Barcelona the airline not only pays no VAT, but is also exempt from kerosene tax. If you make the same journey by train, the rail company will pay an energy tax and passenger VAT. This means higher costs for the company which are usually reflected in ticket prices.
Archived version: https://archive.ph/7Zrur
So wait, is the free market bad or good? Is the argument to nationalize the airplanes too? Or is it to nationalize the rails but not the train companies and let trains compete like planes?
In short, yes.
In long, the problem is very complex and i don’t know how to solve it, having infrastructure in general be run by the government is a good idea, but what is infrastructure and what service? In general rails should be treated like Road, so public property, but of the train company should be a government institution or not is a hard question, there are many pros and cons to that.
Is capitalism bad? No. It needs to be run on a well oiled system and have restrictions, so a social media economy is probably the best option.