I've bought a second hand old Peugeot, I really enjoy the bike, but I'm having a balance problem with it, pulls to the left when riding.
Could it be related with the handlebars? They are crooked.
I have a vintage peugeot and one characteristic of older steel frames like them is horizontal dropouts. Although they have their advantages it also means you must be careful to align the rear wheel properly when putting it back on the bike.
If you look carefully from above the wheel should be exactly central between the chainstays and the seatstays. Although hard to see, in your 2nd photo it looks as though it's off to the left a bit. Just loosen the QR and carefully adjust the axle's position in each dropout until you have the wheel central.
This is most likely the cause of your problem.
http://marksbikes.wordpress.com/2011/01/09/bike-mysteries/ might be a useful link to start with - It says Anjou on it, so its reasonable to guess its a Peugeot Anjou of some year. In that link, they do link to some old Peugeot catalogues and what not (for example: http://i419.photobucket.com/albums/pp271/qeugeot/1989fr/1989fr_27.jpg is a 1989 Peugeot Anjou). Depending on what parts of the bike are original, you may be able to figure out what year it is from the catalogues.