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
This is pointed out in the article, and was even quoted in the very post you replied to.