A common and costly problem on the Saxo (and Peugeot 106) is rear spoke arm bearing wear. To check, stand a few meters behind the Saxo and look at the rear wheels. They should be approximately vertical. If one or both bow inwards at the top, the bearings are damaged. This typically means a new rear axle is required as most shops don’t touch the job and even if they manage to disassemble the axle the axle bearing face is usually too worn for the axle to be successfully rebuilt. Installing a good used axle isn’t a very big job, but it’s getting hard to find good ones these days.
If you find a car with a slight oil leak where the cylinder head joins the block at the end of the timing belt, don’t worry. All PSA TU engines leak there as standard! Budget only for head gasket replacement if he’s going to throw it away.
Aside from these issues, normal purchasing rules apply. Do you have a complete service and repair history? Are there any signs of rust or accidental repairs? Does it look, run and drive well? It has a full MOT (and are the emission test results there?). There’s not a lot of technology in it, but does it all work?
Lastly, I would avoid buying one that has been downgraded as that is also a good indicator that it has been beaten, or at the very least suspension issues are coming.