The Moderate Phase of the French Revolution, so called because of its moderate changes relative to the Radical Phase of the French Revolution, took place from 1789 to 1792. During this period of time, the National Assembly, formerly known as the Third Estate, gained much power through the people of France (see Bastille day). The National Assembly wrote a constitution for France that worked to change many things that the members of the Third Estate (and more radical thinking members of the other two estates) found wrong with the French government.
One of the main concerns addressed in the constitution (the Declaration of the Rights of Man and the Citizen) was that of the absolute monarchy. Louis XVI's power became extremely limited, as did the power of the first two estates (consisting of nobles and the church). In fact, all special privileges (including tax exemption) of the first two estates were removed. The church was further altered by the Civil Constitution of the Clergy, which (among other things) brought many religious positions under the payroll of the state, limiting their power.
For a great deal of time before the revolution, France was divided into multiple provinces, which acted much like the states of the US. They were restructured into 83 departments, all of which had similar area and population. To better promote the trade between departments, internal trade barriers (tariffs) were abolished, and the multiple forms of weights and measurements between areas were abolished in favor of a single unifying system, which we know as the metric system.
During this time, other countries (ruled by at least partially absolute monarchs) were frightened by the idea that local citizens might question their own rule. To try to squelch this possibility, many monarchs went to war against France, aiming to restore the monarchy. This fighting led to the Radical Phase.
Most information from lectures by professor Storch at the University of Wisconsin - Rock County. Additional information from Fourth Edition Western Civilization from 1300 by Jackson J. Spielvogel.