In A Tale of Two Cities, what is the power that has ground the people down? What does this tell us about conditions in France?

Your question is relevant to Book the First, Chapter V, "The Wine Shop."  After a wine cask falls and spills all over the street of Saint-Antoine, the peasants rush to drink it.  Dickens describes them as "Samples of a people that had undergone a terrible grinding...in the mill."  This is the mill that

...grinds young people old; the children had ancient faces and grave voices; and upon them, and upon the grown races, and plought into every furrow of age and coming up afresh, was the sign, Hunger.

Hunger is prevalent throughout France in 1789.  There was a poor grain crop that year and the peasants had only moldy bread to eat, if anything.  The "nobles of great power," especially the ones of the current time--Louis XVI and Marie Antoinette and their court--have oppressed these people through taxes, as well.  So, Hunger is everywhere; it is present in the stomachs of the French people; it is present in their souls as they are oppressed and disinfranchised.

This chapter of spilled wine is metaphoric for the bloodshed that is to come.  And, Dickens uses the symbol Hunger to represent the physical and spiritual hunger of the people who will soon spill the blood of the aristocrats as the red wine spills through the street of Saint-Antoine in A Tale of Two Cities.