I think Robespierre's period symbolizes the inefficiency of the revolution- it was completely factional and therefore returned full circle (ish) to an autocracy. I think Napoleon came to power because the Directory not only saw potential in him, but also a lack of potential in the situation and a need for change.
This is pretty much how I would respond to the question. The French and American revolutions, although similar in time and philosophies, were dramatically different in support. I feel like the French revolution was just as you said- fractional. Each "leader" of the revolution became either too power hungry or too corrupt when he became in charge or just gained too much power.
Napoleon became leader because, well, he gave the people what they wanted. Napoleon pretty much gave the French people all of what they hoped to desire out of the revolution (more freedoms and liberties and getting rid of the established aristocracy), which is why he was able to stay in power. If you keep the people happy, you're pretty set as a leader.