So, basically, it depends on what you mean by "associate."

The Kingdom of England was never considered part of the Kingdom of France or subordinate to it. English kings and property owners were not bound to the king of France under any kind of "feudal" ties. The Anglo-Norman, Angevin, and Plantagenet kings of England, however, were also major landowners within the Kingdom of France. Obviously William the Conqueror was the duke of Normandy, but his descendants acquired a vast swathe of western France through inheritance and marriage, becoming also the dukes of Aquitaine and Gascony and the counts of Anjou, Maine, Nantes, and Poitiers. The English kings (theoretically) owed fealty to the French kings for their French lands, but in practice a state resembling the Cold War prevailed throughout much of the second half of the 12th centuries.

On the lower level, during the 11th-12th centuries, almost all major English landowners were of Norman, Breton, Flemish, or French origin and owned property on both sides of the channel. Because they were subjects of both kings, they theoretically owed loyalty and service to both kings; in practice, these great men were out for their own ends and were more than willing to manipulate, quarrel with, scheme against, and sell out their kings when the situation called for it.

The English kings lost most of their French possessions in the first two decades of the 13th century. Following the death of Richard I, the French invaded and seized Normandy and Aquitaine. Anglo-Norman lords were faced with a choice: abandon their French property and keep their English, or the opposite. At the conclusion of the war, the English crown was left only with Gascony and a bit of Poitou, and the permanent connection to Normandy was severed. However, the English aristocracy would continue to speak Anglo-Norman (a dialect of old French) for at least another century.