The three mottos or pillars if you like of the French Revolution are revealed in the chapter you mention: Liberty, Equality and Fraternity. It is important to realise how central these three foundations are to the creation of France today as we know it. Each of the three is represented by a different colour which makes up the tricolor, or the French Flag, clearly placing them at the centre of the nation's values and beliefs.
Also note how they arose out of the experience of years of serfdom of the French peasantry. The French Revolution, although perhaps more famed for its bloody executions at the hand of "Madame La Guillotine", is also famous for the liberty that it gave to the people of France who were know freed from the shackles of the nobility, the new-found equality they were given in this new nation and the fraternity with which it was to be built upon.
According to Chapter One of Book the Third, there are three mottoes of the French Revolution: "Liberty, Equality, Fraternity or Death." These mottoes are not only historically accurate but significant in this opening chapter since they give the reader some idea of life inside Revolutionary France during this very turbulent period.
For Charles Darnay, traveling through the Republic in 1792, this motto encapsulates his journey: everywhere he goes, he is stopped and his papers checked. In villages and towns, he sees "citizen-patriots" who are armed with muskets and fully prepared to attack if the need arises.
These mottoes, then, reflect the severity of life in France during this period. In terms of the story, they help to create a serious mood and anxious tone, building tension as Darnay makes his way to Paris.
The three mottos of the French Revolution are: Liberty, Equality, Fraternity or Death.