examples
The only successful French colonies I can think of is Quebec or Louisiana, but they're not even countries. Is there a correlation between being a French colony and not being successful?
Here is the UN data on HDI.
In the low HDI category, there are as many French former colonies as British ones. The most common denominator is not the colonizer, but the continent : 75% of these countries are in Africa. Exploitation of the continent for centuries by foreign powers (European of course, but also Arab and Ottoman before) destroyed local political entites before they were able to form modern states.
Some countries on the continent have a higher HDI (South Africa, Algeria, Gabon, Congo), here again I don't really see a distinction between France and other colonists. Note that Algeria (the only colony where France sent large numbers of european immigrant) has a higher HDI that South Africa which had a similar treatment from the British. Civil wars are taking place in several countries, not only former French colonies : Central African Republic, but also South Sudan, Somalia...
==> In my opinion if there was a case to be made, it would be for former Portugese colonies in Africa : long and bloody decolonization wars, sometimes influenced by Soviet interests, do seem to have crippled those countries in particular.
On the topic of poverty in Africa, there are many great answers on the sub, here are 2 examples :
Regarding other examples you mention :
Francis Fukuyama addresses this in Political Order and Political Decay (Profile Books, 2014).
In his telling, the key difference between French and British colonialism was that the British tried to co-opt local elites, only introducing Westminster systems of government when these were demanded by the local elites, while the French tried to impose a standardised, French system as a matter of course. The British preserved (and sometimes strengthened or even invented) local political systems, while the French de-constructed them. As a result, British colonies came into independence either with traditional elites still in place (Brunei, Egypt, the United Arab Emirates), with semi-Westminster systems that were largely constructed by local elites (Malaysia, India), or with fully fledged Westminster systems (Canada, Australia). In French colonies the local political systems had been deliberately de-constructed and traditional elites had either been pushed aside (Lebanon, Syria), or had survived through corruption and negligence in the French administration (Francophone Africa).
At the time of their independence, many French colonies either had no local elites, or had elites who owed their positions to corruption. In either case, it was very difficult for local governments to then turn against corruption and gain the legitimacy, strength, and/or administrative capacity that would be needed to turn a former colony into a successful country.
That being said, not every former French colony is "extremely unsuccessful". Vietnam is one of the fastest-growing economies in East Asia, and Mauritius is arguably the most highly developed country in Africa. There may be general trends in the former colonies of particular countries, but it is very difficult to generalise on something like this.
As a follow-up, I think a specific discussion of Haiti's unique circumstances would benefit OP. The blockade and isolated imposed on it after the isolation, in addition to France's approach to colonizing that country deserve a better explanation than I can give, so I'd love to hear someone informed expound on those topics if it feels sufficiently on-point. Thank you!