The Franks were a tribal group in the Roman and post-Roman periods.
They were originally from modern-day Germany and migrated westward, becoming foederati within the Roman Empire, and being allowed to settle in an area (sometimes referred to as Francia) across western Germany and France (to the latter of which they were to bequeath their name).
Their realm suffered multiple partition and repartition, as their tradition called for the division of a man's property among his surviving sons. This complicates the description of their history; something compunded by the fact that they were in the course of acquiring literacy.
Their initial recorded dynasty were the Merovingians (of "Holy Blood" fame), who claimed descent from the classical Sicambri people through a chieftain called Franco.
They ruled from the 5th century until the 7th, but their chief ministers, the Mayors of the Palace, obtained an hereditary position and then deposed their king, replacing him by themselves, the Carolingians.
The first Carolingian (the name is taken from Charlemagne) was Pippin the Short, who was elected king in 751CE. On his death in 768, the kingdom was divided between his sons Charles and Carloman but Carloman preferred the monastic life (something the Almighty clearly approved -- within 3 years Carloman had been gathered to the Life Eternal) and Charles reunified the realm.
From Charles (who was crowned Emperor by the Pope in 800, although there is current-day dispute as to whose idea this was) the dynasty ruled until 987, when the Capetians took over on the death of Louis, son of Lothair, also known as Louis Do-Nothing, Louis the Sluggard or Louis the Indolent, who left no legitimate issue.