What does Padme know of the Sith?

The Sith are public knowledge because the history books would've told them about the Sith Empire during the last galactic war. Padme doesn't believe that the Sith are in charge of the Republic, much less that they've gone after her husband.

No one in the Republic or the Jedi Order knew that Dooku's Sith name was Darth Tyranus. In the novelization, Obi-wan finds out from Grievous. Vader finds out later, I believe. And both Anakin & Obi-wan were out in the Outer Rim looking for Sidious after failing to capture Gunray. The seiges had lead them into searching for the Dark Lord.

 

Even if the Sith aren't mentioned in the Republic history books, Padme surely knows a bit from Anakin's "shop talk" when they are together.

 

Including all the reasons mentioned, Padme probably knows about the Sith since 13 years earlier there was that one who helped the Trade Federation conquer her planet, and chased her around trying to capture her on Tattoine, who she saw when Qui-gon and Obi-wan went off to fight him in the hangar. I believe his name was Darth Maul...