What were the main ideas behind …

The ideals of the French Revolution are Liberty, Equality, and Fraternity. 

Liberty

Liberty or freedom was with regard to 18 the century, liberty meant freedom from all sorts of torture and abuse. Another example of state oppression was the censorship of publications containing criticisms of the monarch, the aristocracy or the church.

Equality

The taxation system witnessed the difference in treatment of different people. There were the bourgeoisie and the Third Estate at that time as the two classes. The bourgeoisie was more reluctant about sharing political equality with the lower ranks of the Third Estate, thereby reflecting the lack of equality among people of those times.

Fraternity

This third ideal which meant brotherhood was the most difficult to achieve out of all three. So this ideal was all the more significant only in the initial stages of the revolution, and as the revolution progressed, this focus on unity and brotherhood quickly got lost somewhere.

Although the above three ideas are the most commonly related to the French Revolution, they do not completely define the French Revolution, which is a lot more diverse.