07 jaguar x-type 3.0 awd
when the car is driving the fan and battery light comes on at the same time........ fan turns off when car is turned off.

 

It is always helpful when seeking forum advice to provide vehicle details such as MY, kilometres/miles, engine size, etc.

 

It sounds like you have 2 separate issues.
1. Battery light: When driving the battery light comes on. Does it come on for a short time and then go out? Does it come on and stay on? If it comes on and goes out it is most likely A. loose or corroded battery connection. Remove , clean and tighten. B. An internally corroded cable causing resistance. Inspect cable at connectors for corrosion and replace corroded ones. C. It is possible that the battery is on its last leg. Have it load tested.

2. Fans running: A. With the engine running and the air conditioning on the fans will run all the time. First insert the ignition key and turn to accessory then turn the climate control off. Start the car and check if the fans come on.They should come on anytime the ac is running, keep in mind that the ac runs even in heat mode to dehumidify the air. Next take a short drive to warm up the car and then park it and let it idle with the climate control in off. The single fan should cycle on and off to keep the temperature stable. If it doesn't be careful and not overheat the engine.
Give all that a try and get back to us with the results.