I love that movie! The crowd scenes are simply amazing, I almost disbelieve that they didn't use documentary footage just because of how many extras would have been required. I could probably spend this entire response gushing over it.
For the sake of clarity, in my answer when I refer to the ‘French’ I will be referring specifically to public figures and policy makers who supported French colonialism in Algeria. Far be it from me to tar Sartre or Alleg with the same brush as men like Paul Aussaresses. Anyway, as to your question:
The short answer is that France was running a racist, exploitative colonial enterprise in Algeria. The consequences of such an enterprise are illustrated quite well in The Battle of Algiers. After World War 2, the French struggle to dominate Algeria was characterized by arbitrary killings, torture and political repression. Such is alluded to in the film when the character Colonel Mathieu asks “Should France remain in Algeria?” and respond “If yes, then you must accept all the consequences.” Indeed, many in France were willing to answer “oui,” and with their answer face all attendant consequences. Such men were those like Colonol Bigeard who saw the French presence in Algeria as part of their mission civilicatrice. As he put it: “We are not making war for ourselves, not making a colonialist war, Bigeard wears no shirt as do my officers. We are fighting right here right now for them, for the evolution, to see the evolution of these people and this war is for them. We are defending their freedom as we are, in my opinion, defending the West's freedom. We are here ambassadors, Crusaders . . .” It’s a fine sentiment, but with the supposed mission civilicatrice beholden to the régime du sabre as it was, colonial policy was more violent than uplifting.
The attitude of the French colonialists to the proper nature of their relationship with the colonized people was longstanding. Even so far back as 1843 Lieutenant-Colonel de Montagnac wrote in a letter to a friend that “All populations who do not accept our conditions must be despoiled . . . In one word, annihilate all who will not crawl beneath our feet like dogs." It was the clear attitude of the French that their civilization was superior, and that without them Algeria was hopelessly lost: despotic and oriental. As Jean-Paul Sartre noted: “This rebellion is not merely challenging the power of the settlers, but their very being. For most Europeans in Algeria, there are two complementary and inseparable truths. That they have the divine right, and that the natives are sub-human.” The French attitude towards Algeria betrayed an outcome predicted by Albert Memmi when he theorized that colonization must always end by the annihilation of the colonized.
It was exactly this which the FLN feared most. The French mission in Algeria, by pressing Algerian Muslims to abandon sharia and other touchstones of their cultural identity created violence not only against the physical person, which is bearable, but also against their identities of self and community, which is not. These things, along with increasing feelings of economic and political alienation caused many Algerians to believe that violence alone would free them.
Additionally, French settlers, the pied-noirs of Algeria, reacted to and fermented violence by the FLN with violence of their own. The government, police and military in Algeria was dominated by white settlers who made torture and repression their regular tool. The Colonel Bigeard referenced above is famous for tying Algerian prisoners hand and foot before throwing them off of planes into the Mediterranean. Additionally, as white Algerian settlers felt increasingly threatened by violence and the threat of disengagement by the DeGaulle government many joined the Organisation de l'armée secrete. This was a secret paramilitary society which engaged in a wave of bombings and assassinations. The mutual hatred of native Algerians and settlers was such that one of the FLN’s most popular and effective slogans was “la valise ou le cercueil” (The suitcase, or the coffin.)
Read Henri Alleg’s The Question. It is the most devastating account of the reality of war and colonialism I have ever encountered.
Also Frantz Fanon The Wretched of the Earth and Alistair Horne The Savage War of Peace
Sorry about formatting, I suck at it.
In some ways, the rebellion had simmered since the supposed crushing blows of the 1870s. If you have a look at Prochaska's small-scale study of Bône (Making Algeria French) he gets at the massive expropriation and impoverishment of the entire countryside in the name of the colons and market production for France.
In the wake of WWII, when more moderate voices for reform began to speak out, they were disappointed or, if they dared demonstrate, were repressed brutally. French attempts to find middle ground were laughable; the 1947 idea (in the Organic Statute of Algeria) for a toothless consultative body wasn't good enough for nationalists because it didn't offer them any meaningful voice; it wasn't acceptable for the colons because it offered a voice at all. While France was trying to redefine itself as something other than an empire outright with the "French Union" in 1946 and the "French Community" in 1958, it faced the problem that the same kind of moderation wasn't acceptable to the 10% settler population in Algeria, which itself had a strange administrative position.
As in many minority-settler colonies--think South Africa (the ANC's move to armed struggle), Kenya ("Mau Mau"), Southern Rhodesia (ZANLA/ZIPRA) here--that led to radicalization and a cycle of violence that pushed people on both sides to significant excess. That's part of what Pontecorvo is describing--how it spirals into total upheaval, but also how even defeat and loss can't stop a truly mass movement from re-emerging.