The Dreyfus affair occurred in France during the 3rd Republic in the 1890s. The backdrop here is the Franco-Prussian war in 1870 which was a resounding victory for Prussia (which would later serve as the heart of a unified Germany) and involved a devastating siege of Paris as well as the annexation of the border areas of Alsace-Lorraine (which had been part of France previously). The war also caused the collapse of the prior French government (the Second Empire) and the formation of the 3rd Republic. As a consequence of all of this the overwhelming sentiment in France in regards to Germany was one of hatred. Think of US and Soviet relations during the Cold War, the French viewed the Germans as their natural and inevitable enemy and the loss of Alsace-Lorraine was felt very keenly.

Into this environment insert an event, espionage on behalf of the Germans obtaining secret military information from the French military. In 1894 a French artillery Captain, Alfred Dreyfus, was put on trial in secret for this crime, convicted, and sentenced to imprisonment on Devil's Island, a penal colony in French Guyana (the Northern coast of South America). It should be noted that Dreyfus had a Jewish mother and antisemitism in Europe was rampant, this will become relevant later.

This event garnered little attention at the time but the family of Dreyfus began working in the press to clear his name, certain that he was innocent. In 1896 the French head of counter-espionage came across evidence that led him to believe that the true spy was Major Ferdinand Esterhazy. Esterhazy was tried by a military court in secret in January of 1898 and found not guilty. Also in 1898 Esterhazy retired from the military and fled the country to live in the UK.

Meanwhile, there was a growing public sentiment that Dreyfus was not guilty of the crime he had been convicted of, and had instead been made a scapegoat. This came to a head in January of 1898 (only days after Esterhazy was acquitted) when famed author Emile Zola wrote an open letter published by a Parisian newspaper accusing the French government of antisemitism and injustice in the treatment of Dreyfus. This is the famous "J'Accuse...!" letter.

Because the details of the trials of Dreyfus and Esterhazy were kept secret it was difficult to make an objective assessment of the true nature of their guilt or innocence. It was instead a matter of relying on other evidence and indications. (One of the key items of evidence in the case was a note or "bordereau" that was found in a waste basket at the German Embassy by a French spy. Extremely questionable handwriting analysis was used to tag Dreyfus as the author of the note.) In broad strokes the case became a rallying point in the cause of battling antisemitism in France at the time. And for that reason became somewhat of a cultural dividing line.

In 1899 the French Supreme Court struck down Dreyfus' conviction. Dreyfus was returned to France from Devil's Island and put on trial again, and again convicted, in a military court-martial, of treason. It should be noted that during this time there were riots and siege-like conditions surrounding the trial, by people who felt that this whole process was a grave injustice. One day after the verdict the Prime Minister offered to pardon Dreyfus, on the condition that he plead guilty. He did so and was pardoned, being released from imprisonment only 2 days later.

Afterwards there were tumultuous changes in French politics and elections as well as military leadership. In 1906 the Supreme Court fully annulled Dreyfus' convictions and he was reinstated in the army as an artillery major where he would serve for a year until his retirement.

Anti and pro Dreyfus sentiment would continue to run rampant for a long period, serving as a proxy for right-wing and left-wing political stances as well as anti-semitic and pro-tolerance feelings. During the period where the "Dreyfus affair" was at its hottest (around the turn of the 20th century) there was a marked uptick in anti-semitic publications, for example.

I should note that I've left out innumerable details here, but in broad strokes I think this captures most of what's relevant. Imagine the OJ trial mixed with Watergate and that gives you a sense of the cultural phenomenon at play.

Adding to this, what did contemporary non-French people think of the affair?