If your PSU will run it, the 1950pro will definetly run NFS carbon quite well.
The box says "450 watt power supply with 30amp on the 12 volt rail assuming fully loaded system". Remember though, that's 30 amps combined across both rails. I'd say you probably will be okay.
Whoops, I just saw you need the AGP version, those specs are from my box for the PCIe version.
Kaotao is right. X1950GT is an excellent buy for your AGP system.
I think processor will not be a dramatic bottleneck, since many modern games uses more GPU resources than CPU ones. Perhaps adding 1GB of ram may stretch your CPU life a bit.
Regarding the power issue:
I have an Xpert Vision 1950GT AGP 512Megs on an A64 3200+ with 2Gigs of RAM, and with my old bulk ugly 450w PSU, the VGA goes almost always all right, even in videogames. Only one flaw: sometimes, turning on the PC, the CRT monitor remained blank (power loss). Very rarely it did so in desktop (in both cases, simply turning off and on the monitor resolved the problem). Strangely, it never did so in videogames (perhaps they goes with reduced perfomance, but i didn't noticed, since they goes very, very fast with all filters activated and with full details in 1280x1024... ).
So you can simply buy an high quality PSU (450W or more is perfect), as I did afterwards, and you will have no problems at all with the 1950GT.
Another one thing: the x1950Pro require more power and output more heat than the GT, since it is clocked at 575/1380mhz against the 500/1200 of the GT (and both are made with 80 nanometers process, with same 12TMUs, 12ROPs, 36 Pixel Shaders, 8 Vertex Shaders). And obviously is another excellent VGA.
The power requirements and heat output of the 1950XT are much greater than those of the 1950Pro/GT, since this killer-VGA has 16TMUs, 16ROPs, 48PS, 8 VS . And is more clocked... (see wikipedia, at "R520", and you will have a complete X1xxx series comparison).