Almost forgot to add.
When you go to re-cable, you need to know, the Simplex levers with the sun around the S have notoriously small holes to hold the cable head, so much so it's common to find heads that were shoved in and are now firmly stuck. Standard cheapie cables have heads that won't easily fit. Shimano's cables will work but will set you back $7-9/ea.
I highly recommend this kit, which is usually $9-12 on Amazon, the shift cable ends fit, and it has all housings and cables to do brakes and shifting, so it's a win-win, you can get all cabling done for $10.
https://www.amazon.com/dp/B00L8NDVD6
Not only that, but the stock housing was black, so it'll fit what's stock, size and whatnot. Be careful with the pulleys/jockeys on the rear mech, they're made of Delrin, it's brittle, they'll crack and are hard to find replacements. The mechs on that bike are solid, especially the rear.
That specific Peugeot-branded crankset has a penchant for the 5 arms on the spider bending. Good, lightweight Stronglight crankset, though.
Don't lose the black plastic spacer on the non-drive side dropout. Trust me.
For those levers, I believe the Cane Creek 144.7 gum hoods are the correct replacement.