No, a good Louis XVI is a powerless Louis XVI. Killing him is just one way of achieving that objective, but there are several other, far less crude way of getting rid of troublesome dictatorial French monarchs. The British had a most elegant method of placing them on remote islands in the South Atlantic.
Now, France doesn't have any islands in the South Atlantic (as far as I am aware of), but there does in fact exist a little archipelago in the South Indian Ocean (halfway between Madagascar and Antarctica) called the Crozet Islands, discovered and proclaimed French in 1772. A rather boring climate, I grant you that, Wikipedia herself states that the temperature "may rise to 18 °C (64.4 °F) in summer and rarely go below 5 °C (41 °F) even in winter." So, it'll be cold and fairly Spartan, but hey, there's penguins there:
A wonderful place for Louis to bring Marie-Antoinette and the children. What, scarcity of food? Well, as we say in Revolutionary France,
let them have cake!
The Call at Crozet Islands - Online Travelling Diary
Discover France: French Colonies - Crozet Islands