Hey there!

To help our resident French history experts, could you perhaps post this map or at least give a date on what time in French history it is showing?

What period are we talking about?

I'm just going to guess that you're looking at a map similar to this one, possibly with part of the Holy Roman Empire visible to the east (such as in this map, though it is 200 years away from the first map).

So a condensed version ... the answer is that large portions of northern and western France were at one point or another controlled by the English kings. William the Conqueror was already Duke of Normandy when he conquered England, and years later, his line lost the throne to the Angevins through the heiress Matilda, daughter of Henry I of England. The Angevins were rulers of Anjou, Maine, Nantes, and other territories south and west of Normandy. Matilda's son Henry II married the Duchess of Aquitaine, Eleanor, and thus came to control a large area along the western coast of France.

Over time, more territories were added either by conquest or inheritance. The Angevin Empire controlled more French land than the King of France, despite being nominally his vassal. Subsequent English kings lost most of this land, but during the Hundred Years' War they regained all of it - so when you see a map from the 1400s, there is significant English land on the continent.

On the eastern side of France in the map I linked you have the Duchy of Burgundy, which was theoretically a French vassal but in reality was an ally of the English during the Hundred Years' War. East of Burgundy was the Holy Roman Empire, which was made up of hundreds of small states, free cities, etc.

So, political maps from the time period tend to be very fragmented. Obviously, over time the French monarchs were able to drive the English out of France, conquer parts of both Burgundy, the Holy Roman Empire, and Italy, gaining its current shape.