Hiya! Is there any topic specifically that you are interested in during the medieval period in France? My background is in government and political institutions to the suggestions I am giving here are based on that. If you have other interests, I can try to provide some other suggestions. That being said, here are two books that I think really delve into the politics and government of medieval France:

The first is The Capetians: Kings of France 987-1314 by Jim Bradbury published in 2007. This is an excellent book, that summarizes the reigns of each of the Capetians Kings of France, their accomplishments, and institutional changes. In doing so, you get a good idea of the history, economics, and politics of the period. One thing that should be acknowledged though is that this book by its nature, focuses on the role of kingship, so to a certain extent it is framed as a great man narrative. I don't think that this is a huge issue, as the French kings were hugely powerful figures during the time and helped build up the modern state, but it is a limitation that you should be aware of.

The other book(s) I would recommend are Jonathan Sumption's The Hundred Years' War, which I consider the gold standard on the topic. This four-volume masterpiece (there is a fifth volume upcoming) focuses on the conflict that came about between England and France upon the extinction of the main line of the Capetians. Sumption focuses far more on history, politics, and government rather than warfare, so you won't find detailed analyses of Agincourt or Poitiers here. But here is excellent at driving home the context of the war and the narratives at play beyond the claims of the Plantagenets and the Valois. The key limitation here is that Sumption is British, and so you will have a lot of background on the English side of the war. However, I find this to still be very useful, and he is thoroughly dedicated to the task, so there is plenty of information on the French side too. I was originally taught in school that the English had a claim to France, they won at Crecy, Poitiers, and Agincourt, then Joan of Arc happened and they lost, so this completely blew me out of the water.

These two works should take you through the reign of Charles VII and the start of Louis XI, who is generally considered the first "modern" era King. They are monster works, but I thoroughly enjoyed them, and hopefully they give you a good place to start. Let me know if you want anything more specific or if this is too politics focused for you. Cheers!!