The story of Arthur comes down to us in a number of ways.  Firstly there is the Welsh stories, for example the Mabinogion.  Then there are stories from Northern Britain and lowland Scotland that largely survived the Anglo-Saxon conquests of the fifth and sixth centuries (for example 'Gawain and the Green Knight').  However the majority of the stories as we find them today are "French" in that they came back to the British Isles with Breton nobles and their retinues, who tagged along with the Normans at the Norman conquest.  These Bretons came from Brittany in northern France, and were the descendants of the independent Celtic Kingdoms of Brittany, Cornouaille, Domnonée and Vannetais, of the 5th to roughly 7th centuries.  These were set up by Romano-Britons just after the fall of the Roman Empire, principally by King Conan Meriadoc of Dumnonia (latter day Cornwall, Devon, Dorset and Somerset in present day England), and would therefore remember Arthur as a ruler of the mother country, fighting the invading Angles and Saxons, as they would themselves resist invading Franks and Normans, themselves relatives of the Anglo-Saxons.  Therefore it was more of a return for the Arthurian stories than an importation.