According to Route 66 it is 486km or 302miles and you would need about 4hours 40minutes to complete the journey.

Mind though that the journey from Calais to my place is about 254km or 158miles and according to Route 66 that would take me about 2hours 34minutes. I did that part in 1hour 45minutes last Friday.

So, let's just say that Calais --> Nürburgring is doable in 4hours with stopping for some petrol and food and not breaking too many speedlimits.