Hmm.
Interesting idea, with a colorful background. Definitely sounds like something the Falisci would do. I'd like to see a more detailed, unique weakness...maybe something about the style requiring a certain degree of Showmanship, which an opponent can see through and exploit to the Swordsman's detriment.
I definitely don't like the idea of having five Knacks, even if one of them is given as a Swordsman bonus (I don't like it in te Fighting Friar school, either). Kinda hard to pick one to be gotten rid of, since they all tie into to the Level Techniques, but since you didn't include Feint as a regular Knack, I vote for losing that one. In its place, you could give the Swordsmanship Advantage as a bonus. Eventually, if Prince Falsci decides he wants to get the School sanctioned, that would get dropped to reflect a more "serious" approach.
Apprentice: Too much, way too much. That Disarm technique is given at Journeyman levels in other schools, and the Feint-Disarm combo would be negated by the loss of Feint (not to mention having an ungodly TN to use successfully). The "Falisci Salute" is a nice idea, but gets to be ungodly by the time you reach Master level, especially when it's applied to a Knack as potentially devastating as Pommel Strike. Maybe make it a bonus of twice your ML in the school. That should be sufficient, especially with the 5-point Advantage (Showmanship) given.
Journeyman: This is much more manageable, if a little confusing. Why would, say, having a 4 in Composer help you strike faster? Hence, the "GM Permission" provisio, which you quite logically included. It might be simpler to just give a flat bonus. How about instead, applying the Showmanship bonus to Tagging and Initiative (it already applies to Taunt). Basically, +5 to Initiative, and a Free Raise on Tagging rolls (along with an extra Reputation point, if it would deserve one). If that seems light, then extend it to ordinary Attacks. At this point, you could also include the aggressive Disarm at 2 Raises Technique...though to be honest, this is something I allow anyone to do, like the 2 Raise to take hold of the weapon...thing.
Master: Nice. Not sure about the Passive AND Active Defense option. Not sure it's bad, mind you...just need to ruminate on it. However, I like the idea overall.
I also have a school, potentially for adoption by the Falisci family, on my website--though it takes a very different approach than this one. You can find it here.
Overall, nice job! I'd like to see how it evolves.
~shadow