How to play European versions of games on the American Nintendo 64

Out of the box, no. The Nintendo 64 has a region lockout chip which prevents NTSC (Japanese and US) games from running on a PAL (European) machine.

However, through the use of third-party devices, most games should work. I personally own a N64 Passport Plus which I use to play Hey You, Pikachu! on my own N64. It basically works by using a second, local cartridge to authenticate with the lockout mechanism.

I don't have first hand experience of this, but according to that Wikipedia article, some games won't work even with this - presumably, they perform additional hardware detection, so they might be hard to do anything about. It may be possible to somehow bypass these through Action Replay codes; I don't know exactly how these games perform those checks.

You could also buy a Japanese N64 and bring that home. You'll need a power converter to make it run on 230V, and a TV which will accept the input, but you could run any Japanese game that way, and any US game if you remove the plastic tabs.

As an alternative, if you have a European Wii, at least some of the games might be available on the Virtual Console, saving you the trouble of messing with adapters.

First of all, NUS-006(01) is the part number of the N64 cartridge (please refer to Maru-chang's introduction page), so it won't help. You have to ask the seller (if possible) to provide the game serial (in NUS-NSMx-xxx format for Smash Bros) to check out the information on that cartridge.

As for European cartridges, not all games support language-switching, however as I remembered (warning: I may be wrong, so please correct me if I did make a mistake): if the second set of the game serial ends with a P (NSMP in your case), then the language can be switched to English. You may need to double check that to make sure.