I am pretty sure you can't store medical data in AWS in France. (if your data actually qualify as medical data according the law, it's hard to know without knowing the details, the exact term is "données de santé à caractère médical" which translates to health data of medical nature)
There, you have to choose from a list of certified providers (thanksfully, OVH is now in the list [1]).
It will probably be different for every country, though you should be able to fly under the radar until you get some traction.
[1] Full list [FR] : http://esante.gouv.fr/services/referentiels/securite/heberge...
Get a EU data-provider!
So there this is not new for us. We are currently using a EU based provider for some of the services and a Norwegian based one for the rest.
We might go for azure now for some processing, but the data we can keep there has to be anonymized to the point where it is almost useless.
Of course if you are encrypting hosted data and AWS has no access to the keys, then that gives comfort over the disclosure. The relevant authorities/local authorities would have to come to you for disclosure of the keys and you would have any protections applicable under local laws...
AWS being excluded from business is exactly what those companies are arguing.
[1] https://en.wikipedia.org/wiki/Microsoft_Corporation_v._United_States_of_AmericaThink business: Do you really want to face the media backlash when your competitor lances the story that the medical data you collect goes directly into the tiny little hands of Trump, and to the NSA?
Since you mention the GDPR, that regulation as with previous legislation contains carve-outs permitting disclosure of personal data to comply with legal obligations, for example assisting in criminal investigations. Also, the GDPR, whilst introducing certain obligations on processors, mainly deals with controllers, which AWS is not.
In terms of the host of your data, the location of the data is of relevance, as is the jurisdiction in which the host is based. It's related to the Microsoft v US litigation. The main purpose of the litigation is to decide whether US entities hosting data outside the US have to comply with warrants to disclose that information (and in the process bypassing local protections/giving you the opportunity to fight in local courts).
If Microsoft is successful in the litigation, they won't have to comply with US issued warrants in relation to data stored outside the US.
If Microsoft loses, then you would be better placed using a hosting provider with no links to the US if you want to reduce the chances of data being disclosed to US governmental authorities.
Edit: grabehs answer is clearer than my own. Thanks.
Any US connection is worrying from a privacy POV.
[1] https://en.wikipedia.org/wiki/Microsoft_Corporation_v._United_States_of_America§4b BDSG, Absatz 2. See https://www.gesetze-im-internet.de/bdsg_1990/__4b.html. The gist is: You can transfer data if you inform and the data protection is adequate. Then Safe Harbor collapsed, that was not the case anymore (also before, protection was not really adequate, but that was partly ignored). Thus Privacy Shield to give a new legal foundation. If now that collapsed as well, transferring personal data to the US will indeed be illegal again.