There's no way to update the billing address of my US bank to a foreign address. My UK bank is in the address of my house there. My French bank is in the address of my house here.

As I said, you get one and only one guess as to how the company in question wants to handle this. I want to buy Minecraft for my kid's birthday. Do I buy it from the US store with my US card because that's where I lived when I set up my Microsoft account? Do I buy it in the French store with my French card (with that US Microsoft account)?

Answer: Both of those will get you permanently banned from buying Minecraft on that account. There's a Secret Third Answer, but there's no way of knowing it in advance (or even after the fact since there is no functional customer support that knows about this issue).