I'm looking for something other than The Inheritance of Rome

Can I ask why your specifications exclude The Inheritance of Rome? Is it because you have already read it and want something similar, tried reading it and didn't like it, etc.? Because the book is a 'straight-up history of post-roman Western Europe' (and then some) for the exact time period you specify, which I'm assuming explains the mentioned time frame.

I'm happy to recommend books, whether for western Europe as a whole or more region specific books, but it might be helpful for me and others to understand the motivation behind the question.