IIRC, the '97 Lumina has only one temperature sensor, and the PCM and the dash gauge share the value (Luminas up to and including '95 has two sensors). Also, turning on the A/C should kick on both fans, regardless of engine temperature, so turn on the A/C and watch for both fans to start. The fan on the passenger side will only start (I think) for the A/C. It may also start if the car starts to excessively overheat, I don't remember exactly.
I would check to see if both fans work first, simply by setting the A/C to max and seeing if both fans start. If the fan on the driver's side doesn't start, either the fan is bad or you've got a wiring/relay problem. If you're seeing a temperature reading on the dash, then the PCM should also be getting a proper temperature reading.
Whatever you do, don't let that 3.1L overheat! I love the GM 60*V6 design, but it does not take well to overheating. They will very quickly warp one or both heads, and you'll be up the creek.
If you still can't get it sorted out, let me know and I can dig out my '97 W-car service manual.