Edward I of England was also the Duke of Aquitaine and therefore regarded as a vassal of the French King Philip IV due to what I assume was some odd law, which meant Edward had to pay homage to him during a visit to France. Can someone explain how this is supposed to work when the two men are leaders of independent realms of the same 'rank' so to speak? I would have thought the Duchy of Aquitaine would have been seen by contemporaries as absorbed by the English crown after being passed from Eleanor of Aquitaine to her heirs the future English kings.
As I already mentioned I expect there was some law(s) that enforced this strange situation, can someone explain what they were? I also assume being a vassal of France meant Edward was also required to pay tax to the French king just as the other French lords did?
My only guess for why this happened was because Aquitaine was seen as a de jure part of the Kingdom of France despite being controlled by the English, instead of actually being a part of the Kingdom of England.
The simple answer is that feudalism, lordship, vassalage, homage, and fealty can be quite a bit more complicated than most people realize.
At its most basic level vassalage was a mutual obligation between two individuals, wherein one individual - the vassal - provides service (usually military) and the other - the lord - provides land or other privileges. The outward symbol of this relationship was the paying of homage and fealty. Paying homage to someone made them your "liege lord": the single individual to whom you owed military service. Paying fealty was somewhat less meaningful and was essentially a commitment that you would be faithful to your lord in exchange for the lord's continued support.
But these relationships could get quite complicated. Here's a completely hypothetical example: Duke Henry of Norfolk is also the Earl of Wainford. Wainford is in Suffolk so, as the Earl of Wainford, Henry owes fealty to Duke Robert of Suffolk. Meanwhile the son of Robert, John, is the Earl of Clare (in Suffolk) and the Earl of Swaffham, (in Norfolk). So John (as Earl of Clare) owes fealty to his father Robert (Duke of Suffolk) and (as Earl of Swaffham) owes fealty to Henry (Duke of Norfolk). And Robert and Henry owe homage and fealty to the King. It could get even more complicated when you take into account that all of these men would likely have manors that they had sub-enfeoffed to others who may owe fealty for other possessions to yet more individuals. The concept of a liege lord - the single person one paid homage to - smoothed out some of the complicated relationships, but it could still be quite messy.
So, Edward I was the sovereign King of England who owed homage to no one. He was simultaneously the Duke of Aquitaine, who was a vassal to the King of France (just as William the Conqueror was as the Duke of Normandy centuries earlier) and owed homage and fealty as such. So, the Duke of Aquitaine paid homage to King Philip, but the King of England did not (even though they were the same person, so to speak). In his dealings with the Duchy of Aquitaine, whether it was in regards to taxes, or manpower, or anything else, Edward was the vassal of, and in homage to, the King of France. Things could get even more complicated in practice, but in theory they were ruled as completely separate states.
As you can imagine, this could be a sticking point because of both personal pride and politics. Edward II actually had his son made the Duke of Aquitaine so that he would have to go pay homage to Charles IV instead.
This state of affairs with England and Aquitaine (and England and Normandy previously) is called a Personal Union. The two areas are ruled by the same person, but remain independent with respect to boundaries, laws, etc. This is the same state that the United Kingdom is in today; it is a Personal Union of England, Scotland, Ireland, and the Commonwealth Realms. All are under the same monarch, but operate more or less independently.