In short, the actual person, assuming he existed (which is debatable) had limited/no connection to France. However, that said, I will go over where this stems from.

There are two main reasons you hear about it from the french perspective.

1. The British kingdom of Armorica http://en.wikipedia.org/wiki/Armorica#/media/File:Britonia6hcentury.png

It is said by some that Arthurs earlier years as a warlord were spent in Armorica fighting franks. Armorica was kind of special because much more is available in primary sourcing than basically the rest of Britain from that era. At least sources that arent Saxon (and Saxons wouldnt really want to glorify Britons). The Fall of Armorica is a fairly famous event in frankish history because of the supposed wealth of the country and the nature of the fortress of the capital was difficult to take. Given that the Franks would rule for several hundred years after this point it was a well told story across france. Especially because some frankish storiess claimed Arthur died in the defense of Armorica. (despite the fact that their is almost no evidence that Arther ever fought there). This is also highly controversial, because Armorica fell in the 6th century, and most primary sources put Arthur in the 5th Century.

edit. Pic of what the island looks like now, but was where the Armorican capital (which name escapes me atm) was located. As you can see, pretty epic. http://www.mysticalfrance.com/MontSM1111.jpg (Le Mont-Saint-Michel Monastery, in case you want to look up more pics) (Keep in mind this is a rumored location of the capital. But it could have just been a good fortress. Some historians argue that it wouldnt have been the capital because it at the very edge of the Armorican peninsula and would be exposed to attack, also that alot of territory would have been surrounded by franks for a long period of time before it fell. )

2. the Second reason, and by fair the most important one was french poet Chretien de Troyes. He was a fairly famous 12th century poet. It is likely he drew from welsh mythology surrounding Arthur. But he is the main source of all the modern names and stories. Including Lancelot, Camelot, Galahad, Percival and so forth. He used the Arthur story from welsh mythology made it more romantic, enjoyable, and honorable and it became more famous in france than it did in the remaining kingdoms of Wales. Four of these stories are complete; Erec and Enide (c. 1170); Cligès (c. 1176), and Yvain, the Knight of the Lion and Lancelot, the Knight of the Cart, both written simultaneously between 1177 and 1181 He was also responsible for some of his more glorious stories, along with another author from the 15th Century - Sir Thomas Malory who wrote "le Morte d'Arthur". Malory had Grail stories, round tables, merlin, enchanted swords etc.

So to conclude, a Frenchmen heard the welsh stories, thought it would make a good poem, so enhanced it and added to it until it became what it is today. Fantasy. Most of what is known as the Arthur legend today was developed In France, through French story telling.