The law in France may be different but you have sold the car in Northern Ireland and the deal was transacted in NI and hence, the laws of Northern Ireland apply. The applicable law is the Consumer Rights Act 2015.
Parts of the Consumer Rights Act do not apply to private sales and satisfactory quality is not one of them.
Having said that, it is a criminal offence to sell a car which is not roadworthy but a problem with the engine does not make it not roadworthy. It would cover tyres steering brakes and suchlike, basically anything for the MOT.
BUT you must not misrepresent the car.
So if you said the car was in good condition, or it had no known faults or something like that, then he may have a claim
If you said, “there is the car, try it, save you like it but I know nothing about it” then he does not have a claim.
So it all comes down to whether there was a fault which you declared or didn’t declare or whether you just didn’t say anything about the car at all.
There is also the point here that he has driven the car and was satisfied with it and he drove further from Northern Ireland to France, it seems that it’s been driving okay for a period of time and you obviously have no control over its use during those several hundred miles.
There is another issue of course and that is that if you don’t give him his money back, he is going to have to issue proceedings in Northern Ireland and that might not be particularly convenient for him.
Can I clarify anything else for you?
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