Not having the debt will be a major benefit - but on the other hand, this Haiti will have suffered yet another destructive, scorched-earth war. Also, I suspect that Charles X will lose the war with bad grace and that there will be no formal peace treaty or recognition of Haitian independence, so Haiti will remain in an international legal limbo some time longer than OTL. What might really make the difference is a better-regulated domestic economy and access to Latin American markets.
Countries can do just fine without official admission of sovereignty by the former metropolis. If I am not mistaken, Spain took until late the 1800s to recognize Chile, Peru and other countries.
Provided, of course, that the former colonial power is inable to relaunch a reconquest... France (fortunately for the Haitians) might not be in a position to do so.