Short answers, pulled from the story.
Paths of Glory is based on the 1935 novel of the same name by Humphrey Cobb, which was itself based on the Souain corporals affair, a real incident in which four French soldiers were executed in 1915 under General Géraud Réveilhac for failing to follow orders. The soldiers were exonerated posthumously in 1934.
The French government objected strongly to the film's negative portrayal of the French military and placed enormous pressure on United Artists, the European distributor, not to release the film in France. The film was not shown in France until 1975, when anti-war attitudes had shifted sufficiently for a release to proceed.
Paths of Glory was filmed entirely in Bavaria, Germany, primarily at the Schleissheim Palace near Munich, because the film could not be shot in France due to its unflattering depiction of the French Army. Around 600 German police officers were used as extras for the soldier roles, drawn on for their military training.
Paths of Glory was directed by Stanley Kubrick and stars Kirk Douglas as Colonel Dax, a criminal defense lawyer in civilian life who volunteers to defend French soldiers court-martialed for cowardice. The supporting cast includes Ralph Meeker, Adolphe Menjou, and George Macready.
Paths of Glory received no Academy Award nominations despite a limited December 1957 release timed to qualify for them. It was nominated for a BAFTA Award for Best Film, losing to The Bridge on the River Kwai, and won the Grand Prix of the Belgian Film Critics Association. Kubrick received the Italian critics' Silver Ribbon on the 17th of February 1959, recognizing him as the best foreign director of 1958 for the film.
In 1992, the Library of Congress designated Paths of Glory as culturally, historically, or aesthetically significant and selected it for preservation in the United States National Film Registry.