Well done for starting this thread.
Carolingians are cool. From a war-gaming point of view, they are Saxons with good cavalry. Royal guards look very cool with their red cloaks, white crested helmets and red / yellow shields.
From a historical point of view, the Carolingian Franks (approx 714 AD -888 AD) united / conquered the Saxons, Visigoths, Burgundians, Frisians, Alemanni and Lombards to rule France, the Netherlands, Germany, North Italy and neighbouring lands as far as Barcelona, Rome, Budapest and Prague. They fought the Moors, the Vikings and the Normans and the nomadic tribes such as the Avars.
The Carolingian Franks may well be the historical inspiration for Rohan and Gondor in the Lord of the Rings.
Visually, they are similar to Saxons and could easily be done with a new mini sprue of weapons, cloaks, shields and heads. The shields were round, curved and often studded. The better troops have distinctive bowl shaped helmets and spears with a slightly cruciform point.