I’m often surprised at the ticket prices on trains in Europe. As I’ve traveled around there, it’s not uncommon for me to see a route by train at approximately 100 EUR and the same route by air by for less than half that. Causing additional confusion is that when I take the train, there are often a significant number of empty seats.

It seems that the cost of an additional passenger on a train is almost zero, so why do trains not attempt to reduce per-ticket prices to increase capacity and become more competitive against low cost airlines?

In your example, the train from London to Paris in my experience has almost always been nearly triple the cost of a flight.