Which of these Crusades was fought against European Christians?

The Albigensian Crusade (1209 – 1229) was against the Cathars, a group of Christians in the Languedoc area of southern France. The military campaign, launched by Pope Innocent III, took the lives of between 200,000 and 1 million Cathars and others.

Most of the Crusaders were Frenchmen, sent by the French monarchy. The war was considered primarily political, as it brought the county of Toulouse out of the influence of Barcelona and under control of the French crown.

The Cathars were Catholics who opposed the materialistic excesses of their clergy. They wanted the church to embrace perfection and poverty and preach the message of Christ. Many Cathars lived in the city of Albi, which yielded the name “Albigensian”. The pope negotiated in vain with the "heretics", and then offered the Cathars’ lands to any French nobles who would fight them.

A defining moment of the Crusade: On July 21, 1209, Papal Legate Arnaud Amalric demanded that Catholics leave the town of Béziers and that Cathars surrender. They did not. When asked how to tell Cathars from others, he reportedly told his troops, “Kill them all. God will know his own.” Nearly 20,000 residents, including women and children, were killed and the town was burnt down. In a letter to the pope, Amalric expressed no concern about those killed, including loyal clergymen slain “in font of their own altar.”

The image is of Innocent III in Purgatory, from a vision of the deceased pope begging a nun to pray for his soul.