This would work the other way around in practice (source: Snowden): the NSA would voluntarily give the data that the French want off of AWS in exchange for what

This would work the other way around in practice (source: Snowden): the NSA would voluntarily give the data that the French want off of AWS in exchange for whatever data the NSA wants from within the French territory. The company wouldn't have to refuse anything, because they wouldn't even be aware that this is happening at all. All the company knows is that they host data on US servers. I mean this is what Snowden described many years ago, it's probably way worse, more legalized and even more automated now.