Unless I'm missing something, which is altogether possible, yes it was succesful and no they shouldn't have kept the French around.
The basic time line is as follows:
Initial revolt under religious leader named Boukman: plantations are burned, French flee to coastal cities.
Francois Dominique Toussaint organizes military forces for slaves, I wish I knew more about how he organized this all I've seen is a theory that many of the slaves had been trained soldiers in Africa, and plays off interested European colonial powers against each other. Eventually he becomes consul of Haiti, apparently most of the action was on the Dominican Republic side of the island, and is beloved by both French and former slaves. Eventually Napolean decides to unseat him and sends an army to do so. Toussaint engages in a guerilla war, eventually making peace and keeping it until the French betray him. He dies in prison.
Under a new leader, Dessalines, the slaves resist French forces under Leclerc and then Rochambeau all three leaders pursued policies of attrocity. Supposedly the French just slaughtered anyone they found who wasn't French and Dessalines just slaughtered opposition. Either way it looks like both sides were actively destroying non-combatants. Rochambeau surrenders on November 28, 1803.
It looks like at least one of the deciding factors of the success of the revolution was that they did it during a time of great internal and external danger for France, Napolean wasn't in much of a position to support the French forces once he had sent them, though the initial government under Toussaint seemed like a pretty interesting compromise and success in its own right that France bungled horribly.
Here's a site, its spin is pretty obvious, but it's also nicely concise and has far less of it than you are generally likely to find on the internet.
http://www.wsu.edu/~dee/DIASPORA/HAITI.HTM
Here's something equally good from the other side:
http://www.csmonitor.com/2004/0323/p15s01-bogn.htm