This is my second attempt at interpreting the technique. For my first attempt I was too biased by my Italian training. Having revisited the material, I now see that it is more like small sword techniques, as applied to the long rapier.
First Mistake: This Illustration is of the Parry
Note the lack of blood splatter. This means that the fencer on the left has successfully parried the initial attack.
I was mislead because I was taught to always parry with the point online. Using L’Ange’s method, that rule isn’t necessary.
Single Time or Double Time? Yes.
When you perform the parry and riposte, your blade makes two actions. The first the is parry itself. Lay your sword across the opponent’s blade, point well off-line and true edge slightly to the right such that the pommel forms a straight line with the wrist and forearm.
This is an easy parry. Rather than forcefully pushing his blade offline, you are just using the weight of your extended sword to defend yourself. (It’s downright lazy if you ask me, and that’s a good thing.) As you do this, shift your weight from the rear to a neutral balance.
As soon as your opponent misses he’ll want to recover. As he goes back, you thrust in Quarta. You may step with the right foot as necessary, but you’ll find that a simple lean is often enough.
You can’t really categorize this in terms of stesso-tempo or dui tempi. While the blade is making two distinct actions, the body should make one fluid action with the weight smoothly shifting from rear to front. (The optional step is just a continuation of the weight shift.)