Skipping a few centuries and some Roman name and border changes, we find the Royal Frankish Annals refer to the "Wascones" in the area. The w=g linguistic link (William=Guillaume, warranty=guarantee, warden=guardian) that we find suggests that the Wascones turned into Gascons; hence the name Gascony.
In 1152, Henry II married Eleanor of Aquitaine. Aquitaine was by this time a much larger area that included the Duchy of Gascony, and was now in the hands of the kings of England. Henry's grandson, Henry III, personally went to the Duchy of Gascony to look into mismanagement by the not-always-faithful-to-Henry Simon de Montfort. While in the area, Henry arranged the marriage of his son Edward (later King Edward I) to Eleanor of Castile, half-sister of Alfonso X who had been making claims on Gascony, since it was adjacent to his own territory. Alfonso renounced his claims as part of the marriage contract, and aided Henry in dealing with rebels living in the Pyrenees.
Even today Gascony is France's most rural area; then it was so little populated that Edward I decided it needed peopling, and he sent his men to create villages called bastides so that the land was not going to waste.
In 1328, when King Charles IV of France died, his nearest male relative was the son of his sister Isabella, King Edward III of England. Having the English king inherit the throne of France—although perfectly legal according to Salic Law—did not sit well with France, and so they ruled against it. Edward objected, the Hundred Years War began, and in 1453 Gascony became permanently French.
I want to offer a brief biography of Edward I next.