I think the simplest answer to your question is that the Carolingian cycle (tellingly also known as the Matter of France) is set in and pertains clearly to the mythical and factual history of France, whereas the Arthurian cycle (AKA the Matter of Britain) is set in and pertains to the mythical history of Britain. I'm personally not as familiar with the individual stories of the Carolingian cycle, as a fellow American and English speaker, but the basic premise was built around Charlemagne, a historical and very influential king of the Franks. He was also the first Holy Roman Emperor and ruled lands stretching into modern Germany, Austria and Italy, but his legacy is firmly claimed by the French as one of their founding dynasties, uniting the disparate kingdoms of France (if temporarily). By contrast, Arthur is a distinctly British legend and his stories are set in Britain, whether he's poised as a king of Roman Britain, of the Celtic or British (Welsh) peoples against the Saxon invasions, or a predecessor to the Norman kings of England. It not only makes sense that Arthur would be more well known in Anglophone folklore because his stories are set in England or Wales- he was actually written to be a symbol of British national identity.

Geoffrey of Monmouth's Historia Regum Brittaniae was by no means the first account of a King Arthur, but one of most popular and defining written works in which Arthur was set as a historical ruler of Britain. Geoffrey melded Celtic folklore with elements of historical figures such as Alexander the Great and Charlemagne himself to create a noble lineage for the Anglo-Norman kings and lords of his own era. Arthur was built up by Geoffrey and other writers as a counterpart to Charlemagne and the French dynasties, to establish a more ancient continuity for the English throne. Arthurian legend is one of the defining myths of the collective British identity, functioning as a sort of early propaganda to show that England had just as storied and worthy a past as France as rivalry between the nations began to grow.

Arthurian legend does also borrow to some extent from the Matter of France, so after that point, whether accounting for national pride or not, why would the Carolingian cycle grow to popularity in France, when its tales could just as easily be subsumed into a more familiar context and the established popularity of Arthur? The tales of the paladins of Charlemagne could become stories of the knights of the round table, and wizardly exploits could be attributed to Merlin instead. As the stories of each cycle were repeated over and over, the key figures became more and more entrenched, so that you hear about some legendary king and his noble order and named sword, and you immediately attribute it to the set of stories you are familiar with in your own language.

(Relevant Sources:Fries, Maureen. The Arthurian Moment: History and Geoffrey of Monmouth's €˜Historia Regum Britannie€ Arthuriana, vol. 8, no. 4, 1998. JSTOR, www.jstor.org/stable/27869401.

Northup, Clark S., and John J. Parry. The Arthurian Legends: Modern Retellings of the Old Stories: An Annotated Bibliography. The Journal of English and Germanic Philology, vol. 43, no. 2, 1944, pp. 173-221. JSTOR, www.jstor.org/stable/27705106.)