In new house construction, all headers are 2x10s doubled, anytime jack studs are landing above another header the city guys will ask for an engineers report which often ends up being a beam of some sort. In a situation like yours the beam would be built into the floor where the rim joist is and then the joists are hung off of that. If it's discovered after the fact like yours it could be worked into the wall upstairs just above the floor , spanning the window downstairs. That would take care of the weight of the wall and roof but you would still have to find some way to hang the floor joists from that beam. You might have got away with hanging the joists off the rim joists but some Half wit cut in to it.