Is my derailleur broken?
"when moving to the largest gear the chain slips and eventually it will come off the front crank"
By largest gear you mean large front, small rear?

I would check if the chain is worn out, before investigating the derailleur. I am  assuming


old bike, no one bothered to change cassette and crankset, so gears are at least as worn out as the chain, probably much more (like 2-3 chain changes and no gears changes);
that if the chain is worn out, for some reason it slips on the front rather than on the rear cog.


If the chain is ok, then time to investigate the derailleur.
Internet may help you, there are a lot of documented restoration projects of old Peugeot with simplex derailleur. Example:


from the site https://peugeotcoursepb12.wordpress.com/ (I do not own or know the owner, just a search and some scrolling on duckduckgo images