If we assume that the fictional events of Don Quixote occur c. 1600, roughly when the novel was published, then we can surmise a few things.
His sword was taken from rusted arms and armour that once belonged to his great-grandfather:
The first thing he did was to clean up some armour that had belonged to his great-grandfather, and had been for ages lying forgotten in a corner eaten with rust and covered with mildew. He scoured and polished it as best he could, but he perceived one great defect in it, that it had noclosed helmet, nothing but a simple morion. This deficiency, however, his ingenuity supplied, for he contrived a kind of half-helmet of pasteboard which, fitted on to the morion, looked like a whole one. It is true that, in order to see if it was strong and fit to stand a cut, he drew his sword and gave it a couple of slashes, the first of which undid in an instant what had taken him a week to do.
If Don Quixote is roughly 50 years old, that would place the age of the weapon at approximately 100-125 years old, so dating from 1450-1500 at the latest. That, plus the fact that he slashes with the weapon, rather than pierces with it, means that he is unlikely to be using a rapier, which would have been the popular Spanish weapon of 1600. In fitting with his knightly pretensions, it would also likely have been a long-bladed single-handed weapon, to be used from horseback. (All this assumes that he was not so delusional that he made use of a completely inappropriate weapon, a possibility that should not be discounted, given the nature of the character.)
Anyway, a single-handed horseman's slashing sword of 1450-1500 would typically have been an Oakeshott Type XVIII, with characteristics such as: