Toulouse played an important role during the Albigensian Crusade. Raymond VI, its count, was a Catholic and a Cathar sympathizer.
The city was besieged several times. The last assault (1217-1218) saw the death of their leader, Simon IV de Montfort. "Simon stopped to aid his brother Guy, who had been wounded by a crossbow, and was hit on the head by a stone from one of the defenders' siege engines (either the trebuchet or a mangonel), apparently operated by donas e tozas e mulhers (ladies, girls, and women). It killed him. The leadership of the Crusade fell to his son Amaury but the siege was soon lifted." (Source: Wikipedia)
The Dominican order was also established in Toulouse during that time. (Founder Saint Dominic's home was at 7 Place du Parlement, which is less than 200 metres from I used to live. There is a memorial plaque on the building.)
The Inquisition settled in the city in the 1230s, via the Council of Toulouse. Its hunt for heretics contributed to crushing the Cathar movement in the 14th century.
Toulouse had its first university in 1229. Its aim was to teach theology and Aristotelian philosophy, and combat heresy. It is also one of the oldest in Europe.