England didn't even exist at the time
They keep referring to the country as "England" in the film, but in fact, England didn't even exist at the time. Before the Germanic invasions that occurred beginning in the 6th century, Great Britain was inhabited by Celts, who were influenced by Roman culture to varying degrees. After the Germanic tribes, most notably the Angles, Saxons, and Jutes, invaded and displaced the local populations, their country in the British Isles became known as "England" ("land of the Angles") and their Germanic language, Anglo-Saxon, became known as "Old English".
King Arthur was, in fact, a Celtic ruler who defended Britain AGAINST the Germanic invaders. Thus, he was specifically NOT English, nor did he speak English.