Prosper-Olivier Lissagaray - History of the Commune of 1871 (1876)
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John Merrick at Verso Books says "Lissagaray's book is the classic history of the Commune, the heroic battles fought in its defence, and the bloody massacre that ended the uprising. Its author was a young journalist who not only saw the events recounted here first-hand, but fought for the Commune on the barricades."
The book is frequently cited and from what I can gather considered accurate. The English translation is done by Eleanor Marx, Karl's youngest daughter, who had a romantic relationship with Lissagaray that eventually ended.