Looks like AMD's current gen. of APUs can handle FO4 alright enough:
https://www.youtube.com/watch?v=wZeaTugvxtA
https://www.techpowerup.com/review/a...-5600g/20.html
You could also go for a used "gaming" laptop. Sometimes you can get a pretty decent deal on laptops but you need to be absolutely certain on the specs because the product lines are a mess. A prebuilt with a decent configuration could also work (though the usual is going to suck with that, PSU, case, HDD/SSD).