Actually Louis XVI was executed for a treason. He was no more a king, but a citizen of country. While the judicial process of the condemnation was already questionable in that time, the slight majority of the French Convention voted for the death penalty. The issue was that Louis XVI promised in the public in front of masses to uphold the Constitution and protect the new liberty and freedom. However, he failed miserably and was seen as a person who violated his oath, and betrayed his own people. However, during the Constitutional monarchy, the royal family was already imprisoned, first unofficially after taken away from Versailles in October 1789, and officially after the unsuccessful flight to Varennes in 1791. After losing the crown and declaration of the republic, Louis XVI was just a private citizen of the republic and treated as such by the government. His execution was not assassination. Even his cousin voted for his execution, and this happened well before the Terror and the rise of the Committees (created three months after his execution), and well before Robespierre was the mastermind behind the Revolution (he did not join the CPS until July 1793).
The execution of Marie Antoinette was not really justified, but it happened at the Terror. Marie Antoinette did not have any official power behind the government before the revolution and during. She was just a womb to bring the future heir of France, nothing more or less. Nothing was expected of her. However, during the Revolution, Louis and Marie became very close and supported each other to death, because neither of them trusted anyone except each other. Louis became depended on her to make a decisions, and she was blamed for everything wrong that was bad behind the country. The revolutionary fever was not her fault or cause, but she became scapegoat. Louis XVI was rather stingy with money and kept her wife spending. He did not had mistresses, nor engaged in huge building project. While Trianon was a burden to bankrupted treasury, it was not significant axe there that bled French finances. The revolutionaries were not sure how to deal with Marie Antoinette, and actually were proposing sending her out of France. However, the terror started in September of 1793, and suddenly she became a good target for show-trial of revolutionary justice. The trial did not want to condemn her, it was already decided before that, and she knew it. But it was to humiliate her in front of public, strip her last dignity, especially her true love and dedication to children. The trial was a character assassination, but Marie Antoinette was not broken, and went under the blade as a proud daughter of the Empress.
The trial and execution of king and queen is well documented, including interrogation questions and answers. The execution of Louis XVI was looked as a sacrifice for the better of the country and Louis saw it way as well (so did later Girondists). They hoped with his death to end violence with the king in France out of control, where tens of thousands of people were brutally killed. The trial and execution of the former queen was carried in a totally different spirit as the French Republic progressed further into military dictatorship.