Being a Sith wasn't a crime and the assassination of a legit head of state was treason. Plus, the Senate and most government bodies were in the control of Palpatine. So, basically, the Republic was going to turn against the Jedi. What were they going to do next? Anything from the canon or legends addressing this?
Senate and most of government bodies were in the control of Palpatine...
Usually this kind of control is tenuous and, once the leader has fallen, loyalties of the followers are replaced by survival instinct. Once it was defaced as a Sith, his support would vanish (imagine that it is revealed that the PM/President of your country has been shown to be a psycho-killer... how long would he keep "control" of his party?) Some of his supporters would be genuinely shocked at having been used, and even those who knew of his secret identity would feign surprise in order of not being next.
Also, while being a Sith was not a crime by itself, being the head of state of a Republic at war with a rebellion publicly backed by a Sith (Dooku) would surely have been enough to make much of a case. Once the links of Palpatine with the rebellion were established, the issue would have been settled.
That said, in the film it does not appear that there is a plan other than "we have just found that our enemy is at our back, so we must react quickly before we are overrun".
I think the Jedi council and Mace Windu were not thinking of themselves when they decided to take action against Chancellor Palpatine - the Jedi were selfless, and were thinking about the safety of the Republic. With Palpatine (and Dooku) stopped, the Clone Wars would have ended, and peace would have truly been brought to the Republic.
Even assuming that Windu and the others were thinking of consequences, it seems there would have been two likely outcomes:
- Senate is convinced that Palpatine was indeed Sith: this actually would have been easy to establish, given other evidence that the Jedi had collected before Anakin turned in the final confirmation.
- Senate distrusts the Jedi: they would have likely put the Jedi Council on trial, with whatever outcome that resulted in. But it would have still put an end to that generation of Sith.
But as it turns out in the Canon, Palpatine had made thorough plans. Not only were the Jedi unable to stop him, but he was able to use their attack against the Jedi, thus establishing the Galactic Empire and becoming Emperor Palpatine.
TL;DR: The Jedi still planned to arrest Palpatine, hoping to put him on trial before the Senate.
Oddly enough, finding out that Palpatine was the missing Sith did not seem to change the Jedi plan at all. Prior to this knowledge, Mace Windu had planned to force Palpatine to give up his emergency powers, arresting him if he refused. Based on the brief discussion in Palpatine's office, that plan did not change:
PALPATINE: Master Windu. I take it General Grievous has been destroyed then. I must say, you're here sooner than expected.
MACE WINDU: In the name of the Galactic Senate of the Republic, you are under arrest, Chancellor.
MACE WINDU and the other JEDI ignite their lightsabers.
PALPATINE: Are you threatening me, Master Jedi?
MACE: The Senate will decide your fate.
PALPATINE: (burst of anger) I am the Senate!
MACE: Not yet!
PALPATINE stands, a laser sword appears out of his cloak sleeve, and he spins toward the JEDI.
PALPATINE: It's treason, then.
At that point, Palpatine leaps over the desk and it all becomes a moot point. We can only assume that Windu and the other masters expected the Senate to side with them, unable to believe that the Senate majority would willingly follow a Sith.
Once the battle was engaged, and Windu had apparently decided that Palpatine was too dangerous to live, it's possible that Windu thought the evidence would exonerate his actions after the fact. Or, failing that, perhaps he thought that his own arrest and incarceration/execution was a worthy sacrifice if it freed the galaxy from Palpatine.