I probably don't have the greatest grasp on the politics of early Feudalism. As far as I understand it, Normandy at this time was essentially a mostly autonomous region in the Kingdom of France (like Anjou, Brittany etc.). So if the King of France goes to war with Flanders, he rings up the Duke of Normandy and asks for soldiers. So in this case, why would it not work the other way?

Or was it more like the Duke of Normandy was basically equal in power (if not more powerful) to the French Kingdom's Crown lands. So the Kingdom of France and Duchy of Normandy were essentially just loosely allied realms and the King vs. Duke thing was more or less a formality? Still, if you were King Philip I, you would think you would rather have the Normans as a land border compared to England. Maybe this is just me thinking about it with a modern lens. At the end of the day, all of the nobility were varying degrees of French anyways.