Why did a republican movement emerge in France in the years 1789-1792?
The short answer, of course, is that the French population felt oppressed by their government and had generally felt so since the Middle Ages, combined with inspiration provided by the successful American Revolution and the writings of Thomas Paine. The general concepts of the Enlightenment also contributed, since in the preceeding century King Louis XIV had revoked the rights of Protestants, instituting a period in which many began more serious criticism of the "rights" and competence of the nobility. These criticisms came not only from dissidents and the poor, but from the middle class and philosophers, most notably Rousseau and Voltaire. Much of this philosophy was used as a cover for the self-interests of the middle class, but the example of these men and the admiration by the French of the American leaders and the concepts of equality and constitutional rights sounded pretty good to those who were downtrodden or felt so in France, who were a very large segment of the population. This plus the admiration of America among a portion of the nobility itself added to the ferment.
The economic causes were more complex. France was a quite industrialised society, lagging only behind England, and wealthier than most European nations. But the concentration of wealth at the top of society left a large class of poor, and the squandering of the money in great opulence by the wealthy in personal aggrandizement did not effectively stimulate the economy. These things led to a credit and cash crisis lasting decades, with France as a functioning nation nearly bankrupt on the eve of the Revolution.
In addition, there was a tradition of revolt in France dating back to the 14th Century. See Barbara Tuchman"s book, "A Distant Mirror" for information on the Jacquerie and other contemporary revolts.
As we have seen repeatedly in history, people in nations often assign all the ills of the country to the political party or the regime in power at the time. In France, especially since the reign of Louis XIV, the Sun King, whose extravagance earned him many enemies and the resentment of the taxed masses, people felt that the monarchy was a cruel dictatorship. The emerging merchant class also resented that they were grouped with the peasants into the Third Estate, which had no voting power, no voice in government.
So, it is understandable that after the Revolution of 1789, a new government was established, one that did not belong to any surviving aristocracy. From 1789-1791 a National Assembly abolished privileges, venality, and "feudal obligations." Ecclesiastical properties were confiscated and the church and law courts were reconstructed. (Before the Revolution, the Second Estate of the clergy was extremely wealthy and powerful.) In 1791 the call for a Clerical Oath of Loyalty brought about a conflict between the new sovereignty and traditional loyalties. When King Louis XVI tried to escape to Paris, civil was seemed near, but the First Assembly maintained control; a Paris crowd was dispersed and the king reinstated briefly before a second revolution when the National Assembly established a republic in 1792. Sadly, in 1793 the Reign of Terror began when the militant organization, the Montagards, gained control.
C'est la vie!