Paris Commune wasn't a communist revolution, tough : whiile you had a really significant ensemble of socialists (in the broader sense, meaning mutualists, anarchists, internationalists, insurrectionists, etc.) it was still dominated by left and radical republicans (neo-jaboins, social-republicans, etc.) which definitely didn't have a great relationship with the formers. It noticably plagued the political management (not only in Paris, but also in Spain in 1873)..
Something similar would require, like in Spain IOTL, first an institutional collapse (rather than economic) and enough left opposition already gathered, and then the emergence of a common program.