Short answers, pulled from the story.
The name Frank first appeared in the 3rd century AD during a period of crisis when Rome lost control of regions near the lower Rhine. Roman authors later used another collective term for enemy tribes, calling them Saxons, though the two terms were not always mutually exclusive at first.
Clovis became the first king of all Franks in 509 after conquering Cologne. He had previously defeated Syagrius in 486 or 487 and killed Ragnachar, the Frankish king of Cambrai, and his brothers a few years later.
Pepin the Short deposed the last Merovingian king Childeric III in 751 and crowned himself with approval from the Pope and nobility, inaugurating the Carolingian dynasty. The unification achieved by the Merovingians ensured continuation of what has become known as the Carolingian Renaissance.
Following Louis' death, the Frankish Empire split between his three sons according to Frankish culture and law that demanded equality among all living male adult heirs. In 870 the Frankish realm was permanently divided between western and eastern kingdoms which were predecessors of later Kingdom of France and Holy Roman Empire respectively.
In 496 Clovis I was baptized by Saint Remi after decisive victory over Alemanni at Battle of Tolbiac. According to Gregory of Tours over three thousand of his soldiers were baptized with him.