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I've owned a few shit Peugeots, the decal on the downtube looks like it's Carbolite 103 (4 or 5 in the image below).
Lite does not mean light. It is their standard gas pipe tubing. But with that frame size, it won't be a problem. It will be those wheels you need to worry about. Look like deep section alu which will likely weight as much as the frame. They hold a ton of inertia so will make it harder for her to set off or go up any incline. Unless of course she's fitter than me which is a very likely scenario.
£150 is about the top end of what you would want to pay for that kind of used Peugeot. Especially if you don't get on with the wheel and end up losing another ton to replace them with something lighter.
Sorry, my poor attempt at humour obviously missed the mark: by "Le Gumtree", I meant French Gumtree.
As mentioned above, it looks to have an external BB which suggests it's an English BB.
I did have a UK spec Pug with the ridiculous seatpost diameter, but Decathlon sold a cheap seatpost that came with a suitable shim: I'll see if I can find it.