I can think of a good few examples of historical fighting styles which made use of a weapon in each hand:-
In the East, the Hyōhō Niten Ichi-ryū school of swordsmanship was founded by legendary swordsman Miyamoto Mushashi, and makes use of long and short sword in conjunction with one another.
This is actually very out-of-the-box in comparison with other, more orthodox schools.
There's also the húdié shuāng dāo, or butterfly sword, of Chinese martial arts. A pair of these were used in conjunction with one another, and this is still commonly taught in Wing Chun, Lau Gar and Hung Gar schools. As seen in a few kung fu movies, and briefly in Jason Scott Lee's 'Dragon: The Bruce Lee story'.
Also there's Daab Song Meu, the Thai martial way of using double swords in addition to a selection of other weapons. More commonly called Krabi Krabong, although Krabi Krabong also includes a variety of other weapons.
Going west, there are a lot more general examples of this approach to combat. In terms of historical fencing, Florentine style or Main Gauche have been used to refer to the use of a second weapon or other instrument.
A dagger or dirk would seem to have been more common than a second sword of similar length than the first. Daggers specifically called Main Gauche daggers typically seem well-adapted for the role, designed in such a way as to aid the parrying and sometimes trapping of an opponent's weapon.
In contemporary or more recently historical material, there has also been a common pairing of tomahawk and bowie knife or stick and knife.
So there would seem to be no practical difficulty with the idea of a fantasy style making use of two weapons at once. The other recurring factor that does seem to crop up is that typically only one of the weapons tends towards any considerable length, or both are shortish in length, perhaps because of the technical difficulties of drawing two long blades at once, let alone manouvering them.