It's questionable whether France's military success was all that overwhelming in the late 18th century. However, France reached its military zenith during the Napoleonic Wars that began at the turn of the 19th century. After losing vast lands in North America following their defeat in the French and Indian Wars (1763), France's fortunes changed when they joined the American colonies in the colonies' war for independence from Great Britain. The United States' victory was financially costly for France, however, and their only expansion was the island of Tobago. The French Revolution offered other nations a chance to claim part of the French empire, but Napoleon's rise to military power--first as an artillery officer at the Siege of Toulon--soon provided him with the chance to stage a coup in 1799. The Republican French victory at Fleurus allowed the revolutionary army to occupy Belgium, the Netherlands and the Rhineland before the peace treaty was signed with the Royalist French and their allies in 1795. Widespread French expansion would occur following Napoleon's rise to power.
From 1792 to 1802, revolutionary France fought a series of wars with other European powers. By the end of that time period, it had achieved territorial gains that the kings of France had wanted for centuries but had not achieved. There are at least two major reasons for this:
First, there is the fact that the French armies were quite large and quite well motivated. The French were, for the first time, fighting for their own country as opposed to fighting for the dynastic ambitions of their kings. The French Revolution is credited with creating nationalism as a major emotional and political force. By creating and playing on nationalism, the Revolution was able to put larger and more motivated armies in the field than the autocracies that were fighting France.
Second, there is the importance of military leadership. Though Napoleon was not yet emperor, it was during these wars that he became the leader of France's military and eventually of France. Some amount of credit must be given to Napoleon's military abilities.
We can say, then, that this French success was due to the size and motivation of its armies and to the quality of its military leadership.