Why was the flight to Varennes so important for French history?

It was important because it represented a major betrayal. Two years after the storming of the Bastille, the Declaration of the Human Rights, and the drafting of a constitution, that flight to join General Bouillé and his troops was evidence that the king refused to give more freedom to his subjects, to have elected representives with legislative power, and refused to be the King of the French. He pretended to accept it but wanted to remain an absolutist King, and was ready to send troops to supress what the Revolution created. From that moment on he could not be trusted any more and was put under house arrest.