The 2004 ford taurus' o2 sensors should be found near the firewall before the catalytic converter and near the radiator after the cat. from underneath the vehicle locate the exhaust down pipes that eventually "y" into one assembly. the taurus' o2 sensors are positioned on the downpipes which each are installed with catalytic converters. the sensors form a valuable link in a vehicle's emission and ignition systems by monitoring the amount of unburnt oxygen exiting the exhaust pipes. when working, they help to maintain optimal fuel economy and firing. when a sensor starts to fail or become d***y, readings will be compromised, causing the car to run too "rich" or too "lean" and can result in rough idling, reduced gas mileage and mis fires.
The o2 sensor for your ford taurus is located in your exhaust pipe.