The existing political authority was based on absolutism and the people in charge were monarchs who exploited the people and made many bad mistakes which harmed their respective countries. They also only cared about their personal wealth and lives and didn't care about the people at all.
The french revolution wanted to end this and they were inspired by enlightenment philosophers who believed that power comes from the people and not from the divine will that chooses monarchs. This inspired people to change the government and put in a new republican government which would be based on suffrage and end of tyranny.