What franchise QB are you talking about? Hackenberg is Jay Cutler with worse legs. Cook isn't going to be a franchise QB. Who's left? Cardale Jones, nope. Dak Prescott? Doubt it. Maybe Jared Goff. I'd rather keep Cutler (while not an elite QB, not the bear's biggest problem) and fix one of the lines.
You can take Tunsil out of Ole Miss or Stanley out of Notre Dame at OT. You then move Long back to Guard and take Tuerk from USC, Jack Allen from MSU, or Dan Voltz from Wisconsin in round 2/3 Bushrod, Slausen, Allen, Long, Stanley could be a line that allows Cutler to get comfortable.
Or you can go with Bosa or to play DE or Robert Nkemdiche. Personally, I'd play Nkendiche as a 3-4 DE. I'd expect Bosa to be more of a pass rushing DE like JJ Watt, while Nkendiche is the big guy who takes up blocks at DE like Richard Seymour. That will help out the defense a lot. You need lineman to run a 3-4.