Mostly, as French genealogy researchers, we tend to revile the Communards for having burnt the Paris town hall and destroyed hundreds of years' worth of parish and civil registrations. We tend to forget that they were the desperate poor. We tend to forget that they had endured a siege so long, so horrific and in such cold that Parisians were eating dogs, cats and rats, when they could find any still alive. We tend to forget that France had just been invaded and lost the Franco-Prussian War and was saddled with a very heavy bill to be paid to the victor.
The Communards saw themselves as freedom fighters driven by desperation, hunger and poverty to create a new order by smashing the old. Whether we agree with their ideals or not, we cannot help but sympathize with their sufferings and this may help us to understand. (Who among us has not lost judgement when forced to desperation by whatever unendurable suffering life has thrown at us?)
These memories recounted to the press by some of the last survivors of the Paris Commune are fascinating. If your ancestor were among them, it may open your eyes to more of their world.