The magistrates, who go by the Twitter handles of @Proc_Gascogne and @Bip_Ed, did not identify themselves or specific details of the trial in their tweets, France 24 reported Sunday.
An "exasperated" @Bip_Ed joked about strangling the chief judge in the middle of the Mont-de-Marsan courtroom and later suggested killing a court member.
The two judges later speculated together about the legal implications of slapping a witness.
"That's it, I've made the witness cry," one tweeted.
The French newspaper Sud Ouest published the identities of the judges Wednesday, prompting them to close their Twitter accounts.
Supporters said on Twitter the newspaper was wrong to publish the judges' names.
A journalist said the newspaper sacrificed the judges for the sake of a story.
"Who are we to give lessons?" the journalist messaged.
"Freedom of expression of thoughts and opinions is one of the most precious human rights," wrote another supporter.