I don't know how much truth is behind this. But it seems to me that being a left handed melee fighter would bring you at a terrible disadvantage. Not 100% sure but I think in medieval times being left handed was either unheard of, or if it was, a curse.
Think about it, if your fighting someone with sword and shield they have there sword on there left side from your prospective. If you were to have your shield on your right hand your left side would be unprotected giving you a disadvantage. You wouldn't be able to block there swings without turning your body so you no longer face your opponent.
also something to note, many.. in fact most left handed people are only left handed in writing. So you would probably still wield a sword and shield as if you were right handed. For instace the mouse you use for your computer, something tells me you don't use it in your left hand whilst using your right for WASD. (my brother is left handed and had tryed to get used to using the mouse in his left hand to have better aim in FPS but ultimately he found he was to used to playing right handed.)
While I'm better at some things with my right hand (for example, I usually write with my right hand, but if for whatever reason I couldn't use it I'd get by with my left) but most things I pick up are easier with my left. Main reason I use the mouse in my right hand is that's how I was taught when I was a kid, but I can easily use it in my left hand, too. (As a side note, though, I saw a thread about being unable to re-map the numbers on the number pad properly, so even if I were going to go through all that trouble I might not be able to.)
I'm fairly ambidextrous, but it seems I'm closer to the opposite of what you describe.
I do know that in medieval times, left handed people were said to be fighting for the devil, but I'd say it was more of an advantage because pretty much every swordsman (including those who might be left-handed) trained with their right hand their whole life. If they were then confronted by someone left-handed in battle, the same problems that apply to the other person in regards of shields and such apply to them as well, on top of the fact they likely never trained with someone left-handed.