Florentine is a non-period term for using two swords in combat.
Not a demonstratably historical fighting style for battle or for tournament, it does have a basis in reality for late period civillian duelling with rapiers where it is referred to as a 'case of rapiers'. Examples of cases of rapiers have been found, but the extent of their use is debated.
It is an unlikely historical style in either early period combat where a shield is preferable or in later combat where the shield was less necessary due to the more effective armour as a single handed sword is unlikely to penetrate plate harness, and weapons such as the poleaxe gained a greater footing. It may have been an option of last resort.