France, in modern use, refers to the lands which are ruled by the Franks.
Historically, the Franks were still a Germanic people in the Arthurian era and were only beginning to move into Gaul, or had only just done so, depending on when a particular author imagines that an historical Arthur may have lived.
To determine what any medieval author of an Arthurian work means by France it is necessary to examine the work. The Prose Lancelot usually uses the name Gaul instead of France. The Prose Tristan begins with a history of Cornwall and Leonois supposedly long before Arthur’s reign, but anachronistically places the historical French Merovignian monarchs ruling from Paris during the same period.