Franken's 'resignation' was politically necessary as a ploy against Roy Moore in Alabama. Sounds strange but I think it really was the case. If Moore won, a definite possibility, the contrast between Franken and Moore would have been stark. There would have been intense pressure not to allow Moore to be seated in the Senate. But since Moore lost, there is less of a political reason for Democrats to have to force Franken out.
There is a Minnesota groundswell to keep Franken as Senator. At least among progressive social activist types. Not the rest of us. And I think that is because he has been a loyal progressive political activist, and that is way more important to them than personal morality.
I think that the witch hunts will continue. The goal is still to take down Trump. When these senators finally figure out that keeping Franken will make the war against Trump a tiny bit more difficult, they will cry the crocodile tears for him but privately tell him he darn well better resign. Besides, his replacement, picked by the Minnesota governor is another progressive with impeccable Planned Parenthood credentials, having been a PP regional director before being Lt. Governor. They really lose nothing with Franken gone. They will keep their eyes on their goal, which is to take Trump down one way or another.
I'm a 'never Trump' guy but I find that the war on Trump is disgusting.