France and its various revolutions are likely the most important focal point in all of socialist, anarchist, and communist ideological debates until (or perhaps through) the Russian revolution of 1917. I mention its "various revolutions" because we should be clear as to what "French Revolution" we're talking about: the 1830 Revolution, the 1848 Revolutions, the Paris Commune, and finally the revolution of 1789 (I'm also excluding several others). Historians and books often refer to the revolutionary period of 1789-1799 as the French Revolution but the term extends beyond that and the importance of these revolutions is necessary to understand the histories of all later left-wing ideologies.
The philosophers and revolutionaries in France also served as the origin of almost every ideology on the "left." The term "left-wing" and "right-wing" derive from the divisions of the National Assembly in the 1789 Revolution, the terms "socialism" (socialisme), "communism" (commun/communisme), "libertarian" (libertaire in French itself, or used initially by English speakers to refer to political ideologies within France), "anarchist" (anarchiste when taken as a self-description rather than its historically negative connotation) all find origin and form within France.
Karl Marx referred to this particular interest in France as the focal point of revolutionary politics to this time, in his book on the role of Napoleon and the revolutionary period of 1789-99 The Eighteenth Brumaire of Louis Napoleon,
France is the land where, more than anywhere else, the historical class struggles were each time fought out to a decision, and where, consequently, the changing political forms within which they move and in which their results are summarized have been stamped in the sharpest outlines... France demolished feudalism in the Great Revolution and established the unalloyed rule of the bourgeoisie in a classical purity unequaled by any other European land.
Pierre Proudhon, a Frenchman himself and the first self-described "Anarchist," tied together in his work The General Idea of Revolution the various revolutions together as through a common thread.
One day, the 31st of May, 1793, you [Businessmen] were taken by surprise and were supplanted by the shirt-sleeved brigade. For fourteen months, the most terrible period that you have ever encountered, the helm was in the hands of the leaders of the mob... In 1793, just as in 1848, those elected by the people—who for the most part were not of the people—cared for nothing but for preserving the rights of property: they cared nothing for the rights of labor. The whole power of the government, outside of its resistance to foreign enemies, was devoted to maintaining your interests... In 1848, the people, supported, as in 1793, by your bayonets, drove an old knave from the Tuileries, and proclaimed the Republic. In so doing, it only made itself the interpreter of your sentiments, drawing the legitimate conclusion from your long opposition. But the people had not yet been initiated in political life: for the second time they failed in controlling the revolution. And, as in 1793, their presumption again aroused your wrath.
Proudhon was not the only one to connect the various French revolutions into a moving history of revolutionary class struggle, Marx had done several times throughout his life.
December 10, 1848, was the day of the peasant insurrection... Napoleon was the only man who had exhaustively represented the interests and the imagination of the peasant class, newly created in 1789... December 10 was the coup d’état of the peasants, which overthrew the existing government. And from that day on, when they had taken a government from France and given a government to her, their eyes were fixed steadily on Paris.
Throughout communist thought is a return to many “stages of history” ideas, where society has attained certain goals and victories. Marx within Capital and other economics works that capitalism was a revolutionary movement, a transformative movement, but one that needed to be replaced with a communist alternative. As such, many communists would refer to the movement as inheriting or stepping beyond the French revolutions into their later proletarian revolutions.
With their eyes steadily fixed onto Paris would come to a breaking point for the revolutionary left-wing in the Paris Commune of 1871. The revolution of 1871 was a revolution of socialist, communist, anarchist, Jacobin, and other various revolutionary worker groups, its existence has been used to affirm all of their ideological beliefs. Karl Marx writing on the revolution would claim this moment was where the workers of Paris "stormed heaven."
The existence of the Paris Commune would go on to change the beliefs of Marx and Engels, who would write into later prefaces of the Civil War in France "if today, we look back at the activity and historical significance of the Paris Commune of 1871, we shall find it necessary to make a few additions to the account given in The Civil War in France," and more directly into the preface of the of the Communist Manifesto,
In view of the gigantic strides of Modern Industry since 1848, and of the accompanying improved and extended organization of the working class, in view of the practical experience gained, first in the February Revolution, and then, still more, in the Paris Commune, where the proletariat for the first time held political power for two whole months, this programme has in some details been antiquated. One thing especially was proved by the Commune, viz., that “the working class cannot simply lay hold of ready-made state machinery, and wield it for its own purposes.”
Mikhail Bakunin, notable anarchist and popular critic of Karl Marx, wrote that the Commune was not a justification for the views of Marx and Engels but instead was a stern rejection of their views,
Contrary to the belief of authoritarian communists — which I deem completely wrong — that a social revolution must be decreed and organized either by a dictatorship or by a constituent assembly emerging from a political revolution, our friends, the Paris socialists, believed that revolution could neither he made nor brought to its full development except by the spontaneous and continued action of the masses, the groups and the associations of the people. Our Paris friends were right a thousand times over.
As you can see, even more than the prior French Revolutions, the Paris Commune was a break and focal point to later theorists, and these battle lines would be fired across time after time. As time progressed and the socialist, communist and anarchist camps continued to form, spread, or dissipate in their various countries, and as such they continued to find themselves evaluating the French Revolutions.
Finally, the 20th century... (continued below)