Françoise is referring to the Franco-Prussian War of July 1870 - May 1871. After Bismarck rose to power in Prussia, he put forward a German candidate for the empty throne of Spain. The move was calculated to upset the French, which it did; they declared war, but were beaten by Prussia at the Battle of Sedan, and the Prussians went on to besiege Paris. France's Emperor Napoleon III was forced to surrender, leading to his abdication and the beginning of the Third Republic. The country lost Alsace and Lorraine to Prussia, only winning them back after the First World War.
The disastrous war led in part to the Paris Commune, an uprising which took place shortly before Proust's birth.
In the 1890s and 1900s France was torn apart by the Dreyfus Affair, a political scandal in which a Jewish officer, Captain Alfred Dreyfus, was wrongly accused of treason. During the trial the French army fabricated evidence in order to prosecute him. The affair divided French society into those who supported the army and those, like Émile Zola in his famous article J'accuse! who condemned its actions. Proust, like Swann and the narrator in the Search, was a 'Dreyfusard', a supporter of Dreyfus. The Affair, and its influence on French society, is addressed in later volumes of In Search of Lost Time.
This line is from the tragedy Phèdre by French dramatist Jean Racine (1639-1699). The line has entered the French language in a similar way to certain oft-quoted lines in Shakespeare ('to be or not to be' etc) in English.