I am a communist myself, but I'm looking for as unbiased a book as possible. I'm really having an unusually hard time finding detailed information about it online.
I haven't read enough books on the Communeto compare this title to others - like you say, they're sort of hard to find - but I've read The Fall of Paris: the Siege and the Commune, 1870-71 by Alistair Horne. It covers the Franco-Prussian War briefly, and both the siege and the Commune in fair detail.
I'll second /u/Evan_Th's recommendation on Horne. If you want a copy, send me a PM, and I'll give you one.