Sorry I haven't had a chance to reply to this sooner, been a bit busy.
First off, I really recommend Parkers anytime you need a valuation of a car. You can get their book in most Newsagents, which will give you valuations of any car sold in the UK up to 10 years of age. Unfortunately you then have to go online and pay to find out the value of older cars.
Anyway, by using their site, I found that the value of your car in a poor state, sold by a private buyer is ?530.
Click here to see this valuation.
I assume this is the car given that that was what you linked to at eBay. Also, I specified the older version as the newer version was over one grand, and the eBay one was the old version.
Looking at that valuation, they say the average mileage of this car should be 70k Miles. So your Mum's car is almost twice that.
It's quite obvious one of the previous owners has done some serious mileage on that car.
I bought my car for ?100 a year and a half ago. When I bought it my landlord at the time was a mechanic. He owed me a couple of favours so I asked him to check out the car for me (this was after I'd already bought it, as it was very much an impulse buy - long story) which he did. It went straight for the MOT and passed straight away just fine. I've had not a single problem since, it's my first car and it's not cost me anything. Except for new front discs and pads for the brakes, which I did myself. And Oil, which I change myself. But it's been great for a year and a half.
Though it's now possibly needing some more work on it, and this is why I'm telling you this story.
When the Mechanic checked it, he said it was fine but that I should run it into the ground. As the car was so cheap, it wasn't really worth spending anything on it.
And it's the same for you. From what you said, it seems you've already bought the car so really it's too late to change your mind.
For ?250 you're not going to get anything special, and especially with that mileage I can't imagine it's got much longer left on it. However, it could - like mine - be a real surprise and last a couple of years (mind you, mine was at 82k when I bought it, but is 14 years old, and also French).
My advice to you is to make the most of it. It's a cheap runabout (especially at insurance group 3). Give it regular oil changes and treat it gently. Don't expect stellar (or in fact any) performance from it. Use it until it dies. If it's got 10 months MOT on it, then the last check was ~two months ago. Which means it should be in running order. If I was you, I'd take it to a mechanic you trust (or one that a friend trusts) and just ask them to inspect it for you. Most of them are happy to do this and give you a verbal inspection, though it may cost 20 quid or so (believe me, it's worth it, especially to check the brakes - if anything else breaks it's not too bad, but brake failure, particularly for a learner Mum, is never a good idea). If that mechanic says you need to spend a lot of money on something, decide if it's actually worth it (usually it probably won't be) and possibly get a second opinion on it.
Basically, it's difficult to say much about the car itself. All we know from what you said is the car model and age and mileage. Although the mileage is extraordinarily high (and the price reflects this), it's impossible to tell how good such a car is (or how long it is likely to last) without seeing it and hearing it.
I have a bunch of things I check whenever I'm looking at a car for myself or for other people, but I think that as you've already got the car it'd be better for you to get a professional's opinion.
Hope that helps a bit.
Let us know how you get on, and what your impression of the car is once you've seen it.
Also, you're right about that second eBay Clio you linked to. Someone's wasted a whole lotta money!