Say he lives long enough to replicate Washington's two terms. What would his presidency look like?
The 1790s are not the 1950s. Just how much do you know about these times?...I don't think so you see politics then weren't that dirty and his affairs were more of a secret everyone knew but no one talked about out of respect.
That's a much stronger and more relevant argument; I'd suggest you forget about the first line and only mention this one. Franklin had indeed won himself a special place in the American heart, for his generations-long sustained advocacy of the rights, dignity, and benefit of the American colonists/patriots. I do believe that even the luminaries of his own generation, who were as much his rivals as his collaborators and had a more realistic assessment of his limits as well as strengths, did respect him.Not to mention Franklin was held in high esteem by the younger generation then, the Republican Generation (1754-1767) who viewed him as sort of the Grandfather of Liberty basically.
As for his cabinet, Franklin strikes me as the kind of guy who would pick a whole spree of vastly different people just because they could perform that task exceedingly well regardless of partyl lines or reputation.