My Mom is giving me her vintage ladies Peugeot bike. Don’t know what model it is or how to go about fixing it up.

It’s a mixte. The carbolite frames are heavier steel but for an around town bike they can be comfortable. There’s just something about a French mixte thoiugh. I have a 1970’s Gitane mixte that I’m trying to finish up.

While mixte frames are generally woman’s models they are also considered unisex.

I’d start with getting new tires and tubes. it might need the rim strips too.

The chain probably just needs a cleaning and you can put it back on pretty much easily.

Most likely needs a complete overhaul. Fresh greased applied to all moving parts. This isn’t crucial, especially if you are only going to ride it every now and then.

You can get new brake/shifter cables too.

I have such a weakness for Peugeots, French things generally are cool as.
YouTube is your friend, although looks like this just needs routine maintenance. If you prefer the written word then Richard’s Bicycle Book by Richard Ballantine serves as a good workshop manual. Usually a few second hand copies online.