Games that say "EUR Region Free"
Are those compatible with US New 3DS's?
Where did you find this info? AFAIK (and I may be wrong here) in the Wii, WiiU, DSi and 3DS games Nintendo actually enforces region lock.
The only exceptions that I know are those Louvre guides and similar content, since they are intended to be used with tourist's 3DS systems.
EDIT: New 3DS actually uses the same system as original 3DS/2DS to region lock games, there isn't any difference in this.
If you want to run games from other regions you will have to resort either on using launchers and patchers to disable the checks (Gateway launcher, pasta cfw and similar solutions) or have cubic ninja to run regionFour on systems that are beyond the 9.2 system menu.
EDIT2: If you are talking about CIA's, if they are EUR roms patched to be region free, they will run on any 3DS that is capable of installing them.