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
I was under the impression the lowest class seats barely break even and they make it up with first class and cargo or if its a low cost carrier there are all those fees you would not get added to your train ticket. So maybe if the trains made it a point to have those same fees they would be cheaper.