What led to the radicalization of the french revolution?

The French Revolution went on for many bloody years due to political radicalism. The radicalism actually originated from several parties with different views; some wanted a British style constitutionalism while others are opposed to the revolution. Among these parties is the far right Jacobin Club led by Maximilien Robespierre. Amidst the chaos of subjecting the King to trial, forming the constitution, threat of war with Austria. The nation was threatened of war by Austria and Prussia if the king is harmed, which made the king look like a conspirator. Threats of war made prices rise, and so the poor and the working poor sided with the most radical party, the Jacobins. The king was executed, and the Jacobins went into overdrive in eradicating anything that is counter-revolutionary.