is the cooling fan supposed to come on when you start car. only right side fan is coming on in my 2000 Taurus. would this need replacing car is starting to overheat

 

I believe both fans come on low when signal is rec'd from PCM that rec'd signal from sensor.
When A/C is selected power is directed to hi speed relay and that opens power to lo speed relay and provides power to both fans for hi speed.
Check if any power at all is coming to fan that is not working. If power is present , motor is defective or possible connection problem.