Six out of the bottom eleven countries (Chad, Mali, the CAR, Burkina Faso, Guinea, and Niger) on the Human Development Index are former French colonies. The CAR is a failed state with an absurd amount of armed groups and rampant sectarian violence, Niger suffers from a lack of healthcare, extremely poor education, and much of the population seems to be trapped in subsidence farming. I remember hearing Mali had the president and PM arrested after a coup, and Chad has extremely poor human rights and is one of the most corrupt countries in the world. In contrast, the British former colonies in Africa (Egypt, Nigeria, South Africa, among others) still have some issues but for the most part are functional states with governmental control and large economies.
Does this owe more to geography (proximity to the Sahara, poor water sources), French colonialism (I recall reading that CAR's crippling colonialism, stripping of resources, and slavery was inspired by Leopold's Congo), or thoughtless borders during the Berlin Conference?
One as to be careful when trying to find who was the "best colonizer."
Colonization is a complex matter, there wasn't a "french colonialism" and a "british colonialism" which was universally enforced all across those countries respective empires. They were massive differences in status between different colonies, and even within colonies. The experience of an Algerian wouldn't have been the same as of a Congolese, and even within Algeria the experience of an integrated jewish local and a remote Berber farmer would have been very differents aswell.
Adding to this is that simply equating the current situation of a country to it's colonial past is a an oversimplification which ignores factors such as geography and the history of the country before and after colonialism.
Now looking at your statement about former french colonies it is both correct, incorrect and oversimplified. For once if you look outside of Africa you will find countries like Vietnam which are doing pretty well for themselves, of course that doesn't mean they owe their relative prosperity to the legacy of french imperialism but if one wants to judge of said legacy by looking at the current situation of the former colonies he must also look at the "better" examples. We can also look at all the former French colonies that France integrated which even if they are on the poorer end of the spectrum when it comes to French standards they are also on average richer than their immediate neighbors.
When it comes to Africa specifically it is true that several former French colonies are among the lowest HDI on the continent but we must take into consideration that those countries also suffer from some of the harshest geographical conditions on the continent, with Chad and Niger having most of their territory in the Sahara and the rest in extremely volatine Sahel where due to erratic rainfall patterns arable land can become unusable on a year to year basis.
Adding to this is the fact that the countries are deeply divided among religious lines with large muslim and christian communities, as the area is a point of contact between muslim influence from the north and christian influence from the south.
However those are not the only former french colonies on the continent, for once France simply has the most former African colonies than any other european countries so it's simply more likely to have countries falling on either sides of the economical success spectrum. And it does have more succesful former colonies, with countries like the Ivory Coast, which is just below Nigeria, or Senegal who are in the continental average and even several at the top. Countries like Algeria, Tunisia, or Gabon rank all in the top ten, with Algeria and Tunisia being even higher than South Africa and Egypt.
Not only that if you look at other datas like GDP growth former french colonies tend to perform better than their english counterparts, dominating the top ten with five entries in it like the Ivory Coast, Djibouti or Guinea.