To buy or not to buy…

Good day together I’m about to buy a new old car. I’ve seen a beautiful 406 coupé for just under 15’000 francs (just under 10’000 euros). 6 years old, silver, V6 with automatic, winter and summer tires on original aluminium, 46’000 km. The car looks absolutely perfect inside and outside. Neither scratches nor dents in the car, the leather is absolutely new and it has always been waiting in the contract workshop where I could buy it with a year warranty. On the test drive has not, glared or creaked, even if I have been whipped around the curves with squeaking tires (ESP off!).What should I pay special attention to? Where are the weak points? Thank you for your tips and greetings from Switzerland Richard