When you say it won't run 'correctly', what exactly do you mean? I'm searching the net as I don't have first-hand experience of this, but it seems like the problem lies more with the TV than the console: US TVs are generally poor at showing PAL content, whereas PAL TVs back in the 90s got very good at displaying NTSC, using so-called "PAL 60". When the Dreamcast came along with the option to play games in 60hz, I'd always pick that. Even a modded PAL SNES can play NTSC games without issue.
So, it sounds like the console should play it fine, but maybe your TV doesn't like what the console is putting out. There are a few options. If a French Canadian version was actually released, as the above post implies, it's damn hard to find. Converting PAL ROMs to NTSC... I dunno. Translating the US ROM? No, crazy amount of work. So the one simple option remaining is emulation. I know N64 emulation is still not perfect, but I'm guessing that Paper Mario runs pretty well on Mupen64Plus.