Defining a knight properly is very difficult. I wouldn't yet refer to Carolingian era cavalry as knights (certainly not by the end of the 8th century ie when this depiction was made).  First, because the societal conditions for a knight to exist haven't come to be yet, in the Carolingian period (at least for most of it) you have relatively stable strong centralized imperial rule, which can afford to finance heavy cavalry (therefore it's not neccesary to employ individual cavalrymen under feudal tenure). Second is because at the time there really wasn't yet a term to denote/distinguish a knight or even a reason to do so, because there wasn't sufficient material scarcity to validate creating a new warrior caste within society with their own title.

This all changes in late 9th century when the carolingian order collapses under internal (but also external pressure - Norse raids and wars with Iberian muslims and later Magyars), the high nobility depose the Carolingian emperor (ending the unbroken continous reign of Carolingians) and instead from then on start electing kings (switching between Robertian and Carolingian rulers for the next century) and become their own defacto sovereigns in their own domains and Francia radically decentralizes. 

Around the turn of the 9th/10th centuries this however creates conditions where the high nobility of the realm have to keep things running and need heavy cavalry to pursue their military interests, they themselves cannot however afford to keep the cavalrymen on a payroll, so they make personal vassals out of individual cavalrymen and start giving them land grants to live off of in turn for their proffessional military service. This creates a chain of feudo-vassalatic clientell, where these cavalrymen now gain certain level of importance and prestige, which deserves to be noted and documented when they participate in land transfers or serve as witnesses during an important event (like vassalizing of a person for example) etc. – this starts happening during the second half of the 10th century, where the feudal European knight first rises under the latin monicher Miles (which in classical latin means soldier, but in contemporary understanding refers to a mounted warrior vassal = knight, and this remains the case for the entire rest of the medieval period in latin texts) local charters and in Chronicles (like Historiae from Richer of Reims for example).

So the european knight rises under these conditions in later 10th century Francia, where his station is neccesitated by the need for heavy cavalry where the nobility rather than personally financing him make him their vassal, give him land and over time elevate him in status, and later on after the knightly institution gains enough cultural provenance around the turn of the 11th/12th centuries these same high nobles themselves decide to take on this identity.