Welcome to the 406 Owners Club (406oc.co.uk and pug406.co.uk). If you havn't registered, you can post in here, and find out what the site is all about!
The main thing I would look for is accident damage. Make sure all the panel gaps are good and the colours are the right shade. The front end is difficult to 'tidy up' after an accident and the panel gaps must be really sweet otherwise the car will look crap here.
Handbrakes are crap on 406's but it should at least hold the car easily enough, and check it pulls evenly on both wheels.
Cambelt change is important.
The air con can give trouble on 406's (not sure if it effects the coupe so much) but the condenser at the front goes after about 7 years. So check the a/c works and ask if any works been done here.
I don't know what else as we don't really deal with coupe's on here. By all accounts though the V6 is a pretty tough old thing giving very little troubles (except the mahoosive fuel bills but I suppose you know this).
Cars in my care:
2021 Kia Spottage 1.6 Pez Turbo Dual Clutch Gearbox Trickery
2013 Renner Twingo - donkey work