German employee with French company car in Germany

Hello all, I received a new service car from my new French employer last week. This car was also registered and insured in France. The company has no branch office, or similar in Germany. However, I will mainly move the vehicle in D, as I will be working here from the home office. Now the problem. The French insurance company probably said that the car should be moved abroad for a maximum of 3 months not to cover insurance. Is it possible to have the car insured with a German company with French registration plates? A registration in D is not possible, because the company has no seat here. I think there can also be problems if for the car no car tax is paid ?!? I am a bit perplexed, maybe someone has had a similar case before?