My driver driving our company car was involved in an accident with another car.

Answer

According to the Shariah, you are not liable for the damages committed by your driver even if he was driving your company's car. He is solely liable for the damages to the other vehicle.

If he was not negligent, then you cannot claim from him for the damage to your vehicle which according to the Shariah is an Amaanat in the possession of the worker. Only if negligence is proved may you hold him liable. If it is the fault of the other car, you can claim damages for your car.