[jfengel]

They didn't have to do in Louis XVI. He had already been deposed, and he had publicly accepted it. He was later tried for treason, and the National Assembly voted to execute him -- by a one-vote margin.

The resulting "republic" instituted a period known as The Terror, followed by the empire of Napoleon. That ended with the monarchy being restored.

In other words, while Louis' monarchy was no great shakes, I'm not sure that democracy did any better.