Brian's conclusion sounds fair enough to me - a couple searches for things like "Toledo side sword" and the like conjure up results that seem reasably close:
Looks like these sorts of blades are considered a transition between medieval broadswords and later "rapiers", and references to them go hand-in-hand with such names as the Spanish espada ropera and espada ancho, and Italian espada de lato (dressing-sword, broadsword, and side-sword, respectively) seem common enough. Search terms like "conquistador sword" and "colonial sword" ought to pull down a lot of this sort of thing.
Apparently this sort of thing is connected to pirates as well, and I suppose that it wouldn't be a stretch, given the light, nimble, practical every-day-cary nature of the thing for it to have been carried by at least fantasy pirate officers and captains: the whole extended family of these sorts of swords certainly fit a swashbuckler theme!
You can see that the hilts of this progression of sworts could vary dramatically between relatively plain, rudimentary "basket" style hilts, and fairly ornate and elaborate hilts of the sort you'd come to expect from "rapier"-style swords, while the blades were progressing from wider, triangular thrust-and-cut blades to long, narrow thrusting blades of the sort we would think of when hearing the term "rapier".