You don't. Such resources aren't typically made available to the general public.
I would keep the plates and transfer to the other car. Either way you will pay more. One of the things that is not clear is that if you are giving up the first car for another car or if you will have two cars. If you are selling the first car don't pay for the new registration and have the new owner pay for it when they buy it. If you are keeping it you will have to pay for the registration and keep the plates because the new car will need both.
how do I find out if a car is insured by just stating the registration number
No. The car must be registered to you.
The French renew their old plates only when the car registration is updated (for a change of the owner's address, or a change of owner). Older cars do not have to switch to the newer "EU plates" in France and the sticker of the country of origin (GB in your case) will be enough.
No
No, typically plates are kept by the owner when selling a car.
In Britain, 'S' registration on cars number plates is for the year 1998.
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Not ordinarily. Each vehicle must be properly registered with the local motor vehicle department and properly licensed. If the plates and registration do not match, one could be subject to receiving a moving violation and be fined. In some states, the license plate is issued to the owner of record and not the car. When the car is sold, the owner removes the plate, which then forces the new owner to re-register the vehicle in their name.
When a car is sold, the license plates typically stay with the car and are transferred to the new owner.
When a car has two licenses plates (one in front one in rear) which plate gets the yearly registration sticker?
no those plates match that car you will get in more trouble for switching plates than not haning any at all