Given the age of the bike and how it rusted, it is probably just mild steel.
mig it and make a small gusset plate to strengthen the area, if its broke once, it may break again, you wouldnt want it breaking again after you've painted/coated the frame
It's not broken, it's rusted through, most likely from lack of paint originally. They were not renowned for lathering it on. The only thing that could have caused a problem there was having a foot peg bracket and he's taken that off. If you can put a gusset on there and make it look standard it would help but it may be a trap for more rust.