A typical fire is not a plasma.
In typical combustion of carbon-based materials there are two colors you're used to seeing: blue and orange/red/yellow.
The blue comes from the gas phase. This is emission from the excited C2 dimer, which is the high-temperature decomposition product of carbon species in insufficient oxygen. The blue color comes from the Swan bands.
The orange comes from very small particles being carried up in the smoke. These come from incompletely burned fuel and include carbon black and various fullerenes. These are emitting light because they're hot (blackbody emission) in the same way a piece of metal glows red when it's hot.