Chain and chainrings look fine and it will be very unlikely that these are at fault. *Peugoet where using the then 'new' narrow chains at the time so there is nothing new.
A few basics first
Put the bike in the a stand and go through the gears and let it freewheel in the stand, or even upside down on the grass the old fashioned way.
If it goes through the gears without issue, they're very likely to be fine but while you are here, check that the jockey wheels move freely
Next check for any stiff links in the chain
And while the wheel is spinning check that wheel actually spins ok and that nothing has tightened up the bearings too much as it turns.
Make sure the tyre doesnt rub.
Makes sure the front wheel moves freely
Next, check the headset moves freely and isnt notchy
Check the tyres are well pumped!
Just bear in mind that these are very basic steel frames and are not meant to set the world on fire, they have their fans but were always at the bottom of the Peugeot range.
Their ride can be a bit lifeless given the tubing material
* a friend wanted to change his Vittoria tyres for Panaracer and found the the Vittorias rolled much better so decided to leave the panaracers as spares.