It partly depends on when in the Middle Ages.

Early on, France did not control much of what is France today. There were periods in the Early Middle Ages, when the Kings of France control really only extended to the Isle de France. Everything east of the Rhone was part of the Holy Roman Empire or the Kingdom of Provence, at various times, Alsace and Lorraine were part of the Holy Roman Empire. Brittany was independent. The South West was independent. Normandy, the North West and Acquitaine were controlled by the Kings of England at one time or another.

The "center of Western Europe" (if people thought that way) would more likely be seen as the Holy Roman Empire, or perhaps Rome, in the Early Middle Ages. It was really only after the French were victorious in the 100 Years War, that it might be possible to think of them as "the center of Western Europe", and that was late in the Middle Ages.