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.
Best Answer
The difference between the American and European version of the N64 console are small but they are different. The biggest difference is American consoles use the NTSC video standard and the European console is designed for PAL. I'm a little surprised that Zelda worked at all, but not surprised that there were issues with the picture.
You need a European N64. I understand there were a couple of models released in France, but really any N64 from Europe should work.