EU's data protection directive and various local legislation like the DPA don't have an issue with the cloud, but are quite stringent on the fact that the data doesn't leave the EU so you are restricted to EU data centers.
Google and Microsoft have services for EU customers that more or less ensure that the data never leaves an EU data center (MSFT guarantees it, google slightly less so) and as far as infrastructure goes most if not all PAAS/IAAS providers have a European data centers. https://aws.amazon.com/compliance/eu-data-protection/
I know for a fact that at the least British, German, Dutch and Italian companies and governmental organizations even in heavily regulated industries like health care and defense use both Azure and AWS for both corporate IT and production (and if we count less regulated verticals such as banking, financial services, and telco then everyone and their mother within the EU uses Azure, AWS, and many other cloud platforms).
So no while there is some issues with some US companies and services in regards to privacy especially around the safe harbor rulings there isn't any global or even meaningful resistance to the use of US services providers and software.
P.S. Also the fact that you use Lotus Notes and Office 2013 also has very little to do with US phobia, you could've used Exchange just as well, and office 2015 just came out and very few organizations have actually migrated to it.
P.S. 2 You've likely already broken your NDA by admitting you signed one or that one exists, as the existence of an NDA is the first thing that is by it. Not to mention that while you didn't gave any technical detail the fact that you've mentioned the restrictions your company and or organization is under is also most likely a breach of any potential NDA as well as organizational opsec protocols.