The first phase of the French Revolution is often characterized as politically moderate. It was primarily aimed, many historians observe, at dismantling the anachronistic privileges enjoyed by the clergy and the nobility, reforming the law code, protecting fundamental liberties, and establishing what amounted to a constitutional monarchy, placing limits on the rule of the Bourbons. While this interpretation makes sense, we should also recognize that these reforms took place amid extraordinary violence in the French countryside, as well as in the cities. French peasants attacked landlords to secure an end to old feudal obligations, and city dwellers agitated, often successfully, for price supports for bread and other necessaries. Additionally, some of the changes instituted by the National Assembly were quite radical in context. For example, the Civil Constitution of the Clergy effectively placed the Church under the control of the French government, and confiscated church lands as security for currency issued under the Assembly's name. The point is that, while the main thrust of the first phase was moderate in retrospect, establishing what we now recognize as liberal reforms, it did not necessarily look like that at the time to Frenchmen.
This said, the "Radical" phase saw a number of extraordinary measures driven both by the demands of the more ideologically radical members of the Mountain and by the exigencies of war. One measure, of course, was to declare a republic by removing Louis XVI from power. Revolutionaries in Paris, goaded by that city's radical sans-culottes, pushed for the elimination of what were perceived as reactionaries, even as the Committee of Public Safety, under the control of radical Jacobin Maximilien Robespierre, made a mockery of many of the liberal reforms of the early Revolution in the name of the war effort. The latter days of this period, especially 1794, saw the establishment of a revolutionary calendar, the adoption of the metric system, the establishment of a national draft, the closing of churches (especially in Paris,) the abolition of slavery in the colonies, and the establishment of a new revolutionary cult.
The phase of the Revolution that saw the rise of the Directory was, of course, largely reactionary. Suffrage rights were rolled back, as were restrictions on the Church and many of the economic reforms of the radical phase. On the other hand, the Directory continued to fight the war, and the national draft, or levee en masse, continued, and the restoration of the Bourbon monarchy was never seriously considered. The Directory succeeded primarily in alienating radicals and conservatives.