Is there any way the Angevin Empire could develop into a real empire? It need not actually be called that name.
Yes, in theory. However, there are some problems with actually pulling it off. It basically comes down to the Plantagenets can probably hold england or france effectivly, but both is difficult. Sooner or later they get distracted in one place and lose the other, as in OTL.
That said, it is doable. My first thought is that butterflying Phillip Augustus away or having him meet some reverses on the battefield (Bouvines seems the logical place to start) could lead to a weakened power base for the French kingdom which leads to an Angevin survival. However, there are several other problems, such as the fact that the Angevins and their descendents had a nasty habit of fighting wars between various branches of the family (from Henry II and his sons down through the War of the roses). A strong central government would probably be needed to pull this off.
One final though, which conflicts with the OP. Maybe some Angevin king decides that the realm is to large to rule as one entity, and splits it. One son inheirets Western france, one inheirits Britain. If you can keep these two kingdoms from bleeding each other to death, then this meets the goal of the POD, in a way. Not a united angevin empire, but two kingdoms, one of which holds parts of france.
One final though, which conflicts with the OP. Maybe some Angevin king decides that the realm is to large to rule as one entity, and splits it. One son inheirets Western france, one inheirits Britain. If you can keep these two kingdoms from bleeding each other to death, then this meets the goal of the POD, in a way. Not a united angevin empire, but two kingdoms, one of which holds parts of france.
If you Ignore the Magic part, The POD is Richard Lion Hearted not Dieing from the Arrow that killed him OTL.The "Lord Darcy" stories by Randall Garrett are a well-known AH based on this premise. However, as they are set in a world in which magic develops as an applied science, it might be too ASB for the purpose of this discussion.
It depends. He was a very accomplished general, but he wasn't very good as an administrator
That wouldn't be what the OP was asking for though. A Kingdom of England and a Kingdom of France ruled separately would not be one Angevin feudal empire, just two nation-states by themselves.