Which reforms did the Paris Commune want in government?

I'm going to guess we're talking here about the Paris Commune that took over the city in 1871 - - the more famous Paris Commune. (There was also a Paris Commune which functioned at the city government of Paris during a portion of the French Revolution, from 1792-1795.)

So let's briefly tell the 1871 story. After the French lost the Franco-Prussian War, the people of Paris got control of the Parisian National Guard cannons that were in the city. The French military could not take control of the city; in fact, some of the military broke ranks with their officers and joined the Paris citizens' commune. The Paris Commune was essentially a socialist form of government, founded by the radical factions (both socialist and anarchist) that had taken hold of the city. They declared Paris an independent commune and wanted all of France to become a federation of such communes, in which all persons had equal status and workers' councils were formed.