Why did the French and American revolutions result in different outcomes? In other words, what problems persisted when the new republics were formed?
One reason was the religious and philosophical foundations of the societies
The philosophical foundation of both revolutions were the French Enlightenment philosophers. However the American revolution was more directly tied to the English Enlightenment of John Locke. Individual rights were thought to be guaranteed by God not so much by the government. The French revolutionaries thought peoples rights came from themselves as the government.
The religious background of the American Revolution was the Great Awakening. This was religious movement that emphasized individual freedom. reliance on the Bible and democratic governance of the churches. The religious background of the French revolution was a rebellion against the autocratic governance of the Roman Catholic Church in France. Voltaire and other French Enlightenment philosophers were atheistic partly as a reaction to the abuses of the Catholic Church.
The religious and philosophical background of the French resulted in a totalitarian dictatorship. The revolutionaries were not accountable to God, the people, or anything but themselves. This resulted in mass excutions of those related to the previous aristocracy, priesthood, and middle class bourgeois who were considered "counter revolutionaries."
The religious and philosophical background of the American revolution resulted in a representative democracy. The Revolutionaries were held accountable to both the people and the laws of God. A government was set up according the the philosophy of Baron de Montiques to prevent any one person or branch of government gaining too much power.
The American revolution was a rebellion against an outside power resulting in a sense of unity in America,
The French revolution was a rebellion against an exiting internal power structure, resulting in class warfare and stress within France.