From the Encyclopaedia Britannica entry for Charles de Gaulle:

De Gaulle's greatest challenge in his early years as president was to find a way to resolve the bloody and extraordinarily divisive Algerian War. France's influential left-wing intellectuals supported Algerian independence and wanted de Gaulle to find a face-saving way to end the war quickly. The European residents of Algeria and their many supporters on the mainland, most of them politically conservative, wanted France to retain Algeria at all costs. The leaders of the Algerian National Liberation Front (FLN), meanwhile, were willing to discuss nothing short of full independence. De Gaulle realized that he had no choice but to end the war, and when he began peace negotiations with the FLN, French military leaders in Algiers turned against him, forming a rebel faction known as the Secret Army Organization (OAS).

In April 1961 the OAS seized control of Algiers and threatened to take Paris as well. De Gaulle responded vigorously, using the emergency powers permitted by the constitution of the Fifth Republic. Most French citizens rallied to de Gaulle, and after a tense standoff, the OAS action fell apart. The bulk of the military refused to side with the rebellious generals, and de Gaulle's peace initiative was allowed to proceed. The bloodletting, however, was not over. The OAS, now a full-fledged terrorist organization, undertook a wave of bombings and assassinations (including attempts on de Gaulle) that left some 12,000 victims. But the overwhelming majority of the population supported de Gaulle, allowing him to negotiate Algerian independence (1962) and defeat the OAS.

Also, from the entry on the history of France (the Fifth Republic):

The new president's most immediate problems were the Algerian conflict and the inflation caused by the war. He attacked the latter, with considerable success, by a program of deflation and austerity. As for Algeria, he seemed at first to share the views of those whose slogan was “Algérie française”; but, as time went by, it became clear that he was seeking a compromise that would keep an autonomous Algeria loosely linked with France. The Algerian nationalist leaders, however, were not interested in compromise, while the diehard French colonists looked increasingly to the army for support against what they began to call de Gaulle's betrayal. Open sedition followed in 1961, when a group of high army officers headed by General Raoul Salan formed the Secret Army Organization (Organisation de l'Armée Secrète; OAS) and attempted to stage a coup in Algiers. When the insurrection failed, the OAS turned to terrorism; there were several attempts on de Gaulle's life. The president pushed ahead nevertheless with his search for a settlement with the Algerians that would combine independence with guarantees for the safety of French colonists and their property. Such a settlement was finally worked out, and in a referendum (April 1962) more than 90 percent of the war-weary French voters approved the agreement. An exodus of European settlers ensued; 750,000 refugees flooded into France. The burden of absorbing them was heavy, but the prosperous French economy was able to finance the process despite some psychological strains.

It's a French problem, then and now.