Describe the most important conflicts between various social groups in eighteenth-century France.

Society in eighteenth-century France was rigidly hierarchical. Broadly speaking, it was divided into three classes or Estates. The First Estate compromised the Catholic clergy. The Church was very powerful in France, and its senior bishops were drawn from noble families. It enjoyed a number of special privileges, not the least of which was exemption from taxation, despite its extensive wealth and land-holdings.
Then there was the Second Estate, the French aristocracy. These were the people who effectively ran France. They had a virtual monopoly on the major offices of state; they supplied the Army's senior generals, and, as we've seen, they enjoyed preferment in the Church. As with the First Estate, they were also exempt from taxation, which created huge financial problems for the French state.
The Third Estate consisted of everyone else; although, there were huge variations in wealth and social status between its members. Some of the wealthier members of the Third Estate, such as lawyers, merchants, and bankers, deeply resented the fact that they lacked formal political power despite paying taxes. Their main grievance under the ancien regime was identical to the American colonists'—they were taxed without enjoying political representation.
It was no surprise that the Third Estate played a leading role in the French Revolution. France's hierarchical society, and the system of privileges it perpetuated, had generated significant tensions which could no longer be held in check. Incapable of meaningful change and adaptation, French society was virtually guaranteed to collapse. Unable to bend, it had to break.