Well, yes and no.
Arthurian texts are divided into two groups: pre-Galfridian and Galfridian. The first category is older, dating at least to the Historia Brittonum, written in Wales in the early 9th century. By this point most of Britain had been conquered by the Anglo-Saxons, with the Brittonic people largely pushed into Wales or migrated to Armorica. Consequently, while many of the early Arthurian sources were Welsh in origin, there is also a number of Breton works referencing him. For example, the Legenda Sancti Goeznovii which praised Arthur as the saviour of the Britons, and the Vita Sancti Paternus which described Arthur as the local tyrant.
Despite this, much of the pre-Galfridian Arthurian sources were undoubtedly from Britain. Moreover, it would be anachronistic to refer to Breton ones as "written in France". Brittany ("Little Britain", as Armorica was renamed into by her new inhabitants) was first a mesh of independent petty Breton kingdoms and later an independent kingdom during this period. After an occupation by Viking Normans, it became the independent Duchy of Brittany that resisted France with varying successes until the 1500s.
The Arthurian legends did not become really popularised until Geoffrey of Monmouth wrote his *Historia Regum Britanniae around 1138. This was likely also written in Wales, but by this point the culturally French Normans had conquered England, and the region around Monmouth was ruled by their Breton allies. Geoffrey himself may have been a member of the new ethnically Breton, French-speaking elite. He drew heavily upon the earlier Historia Brittonum, but weaved a fantastical story that proved to be immensely popular.
Geoffrey's success helped sparked a number of Arthurian works, collectively known as Galfridian texts because of his considerable influence. The result is the emergence of the Matter of Britain - one of the three great cycles of Medieval French literature. These formed the basis of the Arthurian legends as we know them today, and many were indeed written in France.
Nonetheless, many of these works were still produced in Britain, such as Geoffrey's aforementioned seminal work, albeit by French-speaking elites. For example Lanval, an Arthurian lay by Maried de France which, like the rest of her works, was most likely written in England.