The only circuit in Fukui prefecture to drive with your own car is Takasu Circuit. The length of the course is 1533 meter with a straight of 371 meter. It is built to make effective use of the available space so a large part of the circuit is on the inside of the outer part. As such it is possible to divide into two smaller circuits or make a different course layout.
In the case that the circuit is not booked for an event, there are many sessions for free driving. The day has fourteen sessions, from 9:00 am to 12:00 am in the morning and 1:00 pm to 5:00 pm (4:00 pm in winter) in afternoon. A session is 20 minutes of driving and for this the price is 3000 Yen for members and 4000 Yen for non-members. If you book 2 sessions, the price is 4500 Yen for members and 6000 Yen for non-members.
For free driving on the circuit however, it is required to have a course license. There are specific days booked on the circuit schedule during which it is possible to take the license. The cost is around 10000 Yen and if you want to become a member it will be an approximate 20000 Yen additional.
The circuit is not so far from Fukui city, around 30 minutes driving by car. Access by public transport is also very good as there is a bus stop close to the entrance. A trip from Fukui station should take you around 45 minutes to get to the circuit.
A link to the website can be found below:
And a link to the location on Google Maps: