There are two reasons and one non-reason. France during the first decade of the French Revolution was a mess. Many parts of the countryside were revolting against the national government in Paris (often seen not as the French government by the countryside but rather as a Parisian government). In combination, France was at war with Britain to the North, Spain to the South (with Portugal), Prussia and the Habsburg realms to the east, Sweden, Russia, and minorly with the Ottoman Empire.

First, the French was lucky in having competent commanders commanding the French armies. You had people like Moreau, Bonaparte, Kellermann, Desaix, Ney, Massena, and more that fought hard and well for France. They defended and expanded her borders to include Switzerland, Northern Italy, North Eastern Spain, Holland, and parts of Germany & the Netherlands into the French Republic This skill in command allowed France to push back at the enemy to give France breathing space to deal with smaller issues.

Second, the enemies of France didn't fight in unison with each other. The British didn't support the other nations outside of economics, the Prussians, Russians, and Austrians rarely combined forces or marched on an objective with a plan. The armies of France were able to take these individual armies one by one and win. This is what allowed France to dominate the European powers until 1813 when unison of the allies allowed them to defeat Napoleon.

Finally, there's plain luck. This isn't as quantifiable but certainly something to mention. Owen Connelly in Blundering to Glory mentions that Napoleon wasn't a particularity skilled commander but a particularly lucky one. This extend as far back as even the Toulouse campaign. With enough time to defeat the enemy of France and peace, it allowed Napoleon time to make peace with the Pope in the form of the Concordat and thus bring France into peace as it was a deciding factor to pacifying the Vendee.