Might OP's question come from the "Karate-is-based-on-sword-fighting" crapola too often heard from the shoto-hippy-fu crowd?
Find shoto-hippy-fu crowd. Go after them with sword. Clean up after yourself.
Maybe some old school JKD would be more applicable? Bruce Lee was big on fencing footwork though I don't know which type of fencing.
Transfer of Sport specific techniques and tactics will be extraordinarily low to fencing. Attempts to get close to the footwork of fencing will probably just have negative transfer. Your best bets are
1) Improving general conditioning
2) getting more solo practice with your sport skills at a low intensity.
If you are playing another sport, it's to improve general conditioning and athleticism, and that's it. The younger and less advanced of an athlete you are, the more this will help. If you're already a high-level fencer(doubtful) then you need energy system and skill work specific to your sport
Digging around shows that the best correlates of lunge speed are thigh circumference and height on a drop jump. So you should be going through a basic strength training program and moving on to olympic lifts or plyos once you've milked newbie gains.
Street sword or squeegee?
I competed in sabre in college. At the time I was doing a lot of boxing and fencing was sort of an easy workout to do on my off days. It was fun and my rationale at the time was that it was good general reflex training since everything happens really fast.
The moves are really sport specific though and - in my opinion- don't have a lot of crossover with anything else.
If I recall from my copy of Tao of Jeet Kune Do that I haven't seen in 20 years, Bruce Lee took the stop hit and maybe one or two other things as useful from fencing but... I don't know... nothing like that ever seemed to work out in the boxing ring, at least not for me.
But then again I'm no Bruce Lee so take that last bit with a grain of salt.
I still think it might be good for focus and relexes, but I don't think you'll see any useful crossover in footwork or much else.