But he did run for both offices last year, just not at the same time. He ran for president, including in the Florida presidential primary, but then dropped out of the presidential race and ran for Senate (both primary and general) in the same year. So Florida law didn't stop him from being on the *primary* ballot for two offices whose general election dates are the same, yet whose primary dates are different.
Similarly, Rand Paul's "caucus fix" only allowed him to run in the primaries for both Senate and President in the same year, but wouldn't have allowed him to run for both in the general election. Presumably, if he'd won the presidential nomination, he would have dropped out of the Senate race rather than the other way around.
While VP nominees will often want to hedge their bets in the general election, in case their ticket loses, I don't think that's really the case for presidential nominees. Anyone who wins the presidential nomination of one of the two major parties is just going to drop out of any other races that year once the presidential nomination is locked up. What they're really trying to hedge against is that they won't win the nomination in the first place.
So the issue isn't just state law on whether they can be on the ballot for two offices at once, but whether the primaries for Senate and President are on the same date or not, and when are the filing deadlines for the Senate primary. Is the filing deadline late enough in presidential primary season that you might already have a good idea of whether you're going to win the presidential nomination or not? In Rubio's case, he was actually able to run in the Florida presidential primary, then drop out of the race, then file for the Senate primary that same year, because the Senate filing deadline was late enough. But it's not late enough in every state.
I know, for example, that Minnesota has passed a presidential primary for 2020 (was previously a caucus state). Does it still have a separate primary for state offices, including Senate? And is the filing deadline late enough that Franken could run for president, get far enough along in the primary season to see whether he's going to win the nomination or not, and then if necessary drop out and run for Senate?