To celebrate the victory of Austerlitz in 1806, Napoleon decided to erect a monument in the center inspired by Trajan's column in Rome: a bronze column that was forged by melting hundreds of cannons taken from the Austrians and Russians. Just like the Arc de Triomphe, this column also celebrated the victories of the "Grande Armée", which you can see depicted in the spiral of bas-reliefs decorating it. The statue of Napoleon rested on top, but it fared just as poorly as the Sun King's equestrian statue and was also destroyed, not by the French revolutionaries but by Russian army troops who were victorious in the Battle of Paris of 1814.
About twenty years later the unfortunate column was replaced by a statue of Bonaparte, who was first depicted in "Little Corporal" garb and then, at the behest of his nephew Napoleon III, in imperial garb. But it wasn't over yet: in 1871 the column and statue were again taken down, this time by the protestors of the Municipality of Paris, who let them fall on a pile of dung and gave the square its fourth name: "Place Internationale". Everything was restored a couple of years later, and Napoleon was put back to proudly stand on top of the hopefully definitive Vendôme Column.