After seeing what some other folk had done, I thought I'd add in the story of my Peugeot:
A couple of years ago, I bought the first bike I could find that would fit me (I'm a v short-legged woman but wanted a crossbar, so men's bikes that small were a bit sparse) and was cheap and that I wouldn't care about and could lock up anywhere and not worry about, as I'd lent my mum the Trek for a couple of years.
It turned out the first one I found was a mid-80s entry level Peugeot in dubious nick, but was only £15.
Of course, as a bike that I was supposed not to care about, I've become totally besotted with it and would be very sad if it got stolen, so that strategy didn't work at all. It's an absolute joy to ride - the geometry is perfect and just fits and feels great. I put the handlebars on my Trek to see if it was just them, but it isn't, there's definitely something about this whole bike.
It came with some dodgy old one-piece BMX type handlebars that I replaced straight away with North Road ones so I could trundle around looking perky, which I do, often.
I've had vague singlespeed (freewheel, not fixed) aspersions since I got it (I live in the flattest place on earth) and so when I got it, I set the gears into a gear that seemed right and haven't changed it since, so I think I can safely say that'll work ok for me. I'm going to keep all the components in case I want to put it back to geared later.
So two bits of sacrilege planned - I'm thinking of making it singlespeed and I'm thinking of respraying the frame. The former (hopefully) will be done in a non-destructive way so I can always put it back, and the latter, well, the frame's not in great nick with some surface rust and the decals peeling, so hopefully that lets me off the hook a bit. I think having the frame protected by it all actually being covered with paint will be of a better benefit to the bike than leaving it as it is, as it'll rust to pieces otherwise.
Here's a picture of the beast itself - looks a bit weird (my partner's son thinks it's the weirdest thing he's ever seen, although is impressed by the fact it's a Peugeot because that makes it "nearly a car"
So, I reckon a nice classic looking paint job and a nice old single chainset will make the old girl look a bit smart. I want a bike I can love, that's all mine and one that I can learn on - I've fixed bikes ever since I was a kid but I've never taken one apart completely, but I've always wanted to. I imagine there's lots of obstacles in the way but I'll get there. I think it's a new enough Peugeot to have BSA sizing so that should make finding a chainset a bit easier.
Due to aforementioned learning curve and the seven thousand ways this can go wrong, I will not be selling the Trek until the Peugeot's back together and working again...