As everyone has said, movies are entertainment, not sword-fighting training manuals.
There were, however, training manuals (and fencing schools) very early on for those who wished to master the art -- there is at least one German Fechtbuch from as early as the late C13th/early C14th and its quality suggests it's drawing on predecessors -- and these might be worth researching if you are interested in getting the right terminology etc. Done properly sword fighting wasn't simply bash and thump, even with the great swords, as if the blade were no more than a blunt instrument -- there were prescribed stances/guards and defensive and offensive movements.
To start at the beginning, what kind of fighting are you thinking about? For the most part people didn't wander around carrying swords in the C15th, certainly not in the early part of it, so if you're thinking street fighting, then for most it's at best long knives, not swords. (Though the difference between the two can become blurred cf the cinquedea
Cinquedea - Wikipedia, the free encyclopedia) Swords were a weapon of war, and largely limited to wartime use, and remained so for the majority of the population. From
The Noble Art of the Sword by Dr Tobias Capwell (curator of arms and armour at the Wallace Collection in London):
... the wearing of swords in a civilian context was not considered acceptable, so their use in peacetime was only reluctantly tolerated by urban communities. The 13th statute of Edward 1 (1284-85) outlawed fencing schools in the City of London... In 1386 the newly founded University of Heidelberg forbade its students from attending the local fencing schools, a regulation that had to be re-enacted in 1415.
and he goes onto give examples of people being brought up on charges eg "for swaggering in the City with sword and buckler after nightfall". And
It was acceptable to wear a sword ... when travelling, for purposes of personal protection, but wearing swords as a matter of course in an urban environment was frowned upon if not explicitly illegal. Despite the fact that the sword had, by the 12th century (if not earlier) come into widespread use among commoners as well as the nobility, its aristocratic mystique remained... A good sword was still an expensive object; quality steel was a rare commodity and the ability to forge it into a hardened and tempered blade was even rarer. Expert use of the sword required years of dedicated, daily practice, which in turn demanded the sort of time that few could afford.
So your average oik isn't going to have one, certainly not one of any quality.
Secondly, what kind of sword were you thinking of giving your characters? Fighting with a doublehander is very different from using an arming sword, which is different from a cinquedea, which is different from a rapier. Again from The Noble Art
Until the 15th century, swords designed to be wielded in one hand, to deliver both cutting and thrusting attacks, were rarely if ever used by themselves. Rather, the shield was their constant partner... Sword-and-buckler was a highly successful fighting style, remaining popular throughout the 15th and 16th centuries. On the medieval battlefield it was the most prominent non-noble form of swordfighting, while the use of the bigger war swords, the longsword or the two-handed or "great" sword, was reserved for fully armoured knights and men-at-arms.
From the fact you've looked at Olympic fencing, I'm guessing you're probably thinking of equipping your characters with rapiers, which are the go-to swords for films, since they are long and sexy. But these are not swords which were around in the C15th in Europe. By around 1520, men of elevated social status, ie noblemen and perhaps the more affluent middle classes, had begun to wear swords at all times, effectively as another sign of fashion and wealth. The rapier as we now think of it arose from this civilian use, as fashion and the circumstances in which it might be used (not in the melee of war with opponents in armour) brought about a change in blade shape. There's no definitive this-is-the-date-a-rapier-was-first-used since there was a constant evolution, but it's probably not until the 1540s that it's the long thrusting weapon we think of, and as Toby has said, it's the C17th which is its heyday.
Having said that, if you're writing fantasy as opposed to historical fiction, there's no reason your society can't have introduced a rapier-type some 50 years earlier, and frankly I doubt your average reader would worry about it either way.
