== Wrong idea of what a fleche is == 

 I think you have the idea of a flèche (fencing) wrong. You say that the idea is "running as quickly as possible, allowing the attacker to close a greater amount of distance than with a standard attack". That is absolutely wrong. You should never use a fleche to close distance much greater than that of a lunge. You make it sound like the idea is to charge down the length of the piste. Begineers always make this mistake. 

 You should be hitting your oponent at the same point as your back foot has crossed over and hit the ground - well before you start to do any kind of running. You only run because you as you past them you don't want to give them time to hit you on your back. 

 The source you reference pretty much explains this.