Can I buy American AppleCare+ and use it in Europe?
Where can I purchase the AppleCare Protection Plan?


  Depending on the Apple product, the AppleCare Protection Plan is available at the Apple Online Store, Apple Retail Stores, and many Apple Authorized Resellers including many wireless service providers. Apple recommends that you purchase the AppleCare Protection Plan in your country of residence, because each AppleCare Protection Plan has terms and conditions specific to consumers in the country or region in which the plan is offered. Please see the AppleCare Protection Plan Terms and Conditions for complete details.


source: https://www.apple.com/asia/support/products/faqs.html

So Apple provides different protections based on your region of the world and the applicable ToS. 

I was asked to clarify

Apple's ToS for AppleCare is country-specific based upon where its purchased. So if you purchase a US plan, the language includes only language about certain laws in US states where they diverge from the general contract. Same goes for the EU - if you buy an EU plan certain countries have variations on the laws.

That said, from briefly perusing AppleCare ToS, all of them seem to offer the ability to take your device to "an Apple Retail Store" to have it repaired under warranty and no further qualification is given. If you've purchased a warranty outside of your own country I'd presume that that means you can get it repaired anywhere Apple has a store.

I am not an Apple rep nor does this answer have any weight on what Apple actually might do. I'm guessing your intention with this question is to save a few bucks on your AppleCare. In that case, I'd ask if it's worth about the ~15 euros difference in price to protect what is likely a >1000 Euro device?