Microsoft does not have a trademark for "Office", which is clearly a type of product and can't be used as a program name (just like you can't name your oatmeal "Oatmeal" and expect trademark protection).
The only way this would be infringing is if office.eu usage could be confused with Microsoft other's trademarks - like Microsoft Office - but I don't see that.
So no, office.eu will have a calm Monday on that front, just like hundreds of other companies offering products with "Office" in their name.
(I'm not a lawyer. Talk to a lawyer before deciding to take on a trillion dollar company).
Microsoft does have a figurative trademark for "Office" with the rectangular icon: https://euipo.europa.eu/eSearch/#details/trademarks/01141355... - office.eu's logo does not bear any resemblance.
The only way this would be infringing is if office.eu usage could be confused with Microsoft other's trademarks - like Microsoft Office - but I don't see that.
So no, office.eu will have a calm Monday on that front, just like hundreds of other companies offering products with "Office" in their name.
(I'm not a lawyer. Talk to a lawyer before deciding to take on a trillion dollar company).