Thomas-Alexandre Dumas was absolutely exceptional. He was the first black person to become a brigadier general, later column general and eventually division general. He was born in Saint Domingue, what is today Haiti, the son of a white planter and a slave woman. I honestly don't know that much about the status of free people of color in metropolitan France, so hopefully someone could better answer those parts of the question. However, within Saint Domingue they wielded substantial economic power at least.

The top of the social pyramid of were the grand blancs, the owners of the large plantations, senior bureaucrats and allied banking houses. However, to a large and growing extent, the tier below were free people of color. While sugar plantations are incredibly capital intensive enterprises and only the wealthiest could control them, a growing number of coffee and indigo plantations in southern Haiti were owned by free people of color.

An example of this is the story of Thomas Ploy. He was a successful self-made planter. He bought a derelict Indigo plantation for about 2,600 livres, and by the time he finished improvements his property was worth 45,000 livres. He eventually married a white woman from another wealthy family. Another example was that of Marie Bagasse, who was the woman of color who was much better educated and three times as wealthy as her french white husband. I am struggling to find the exact numbers (historians have numbers on this, I just can't find them at the momen), but a large and growing percent of land and slaves were controlled by free people of color including the children of slave mothers, although most of the elite had been free for generations by the late 18th century.

The code noir governed racial relations in Saint Domingue, and while parts of it was racist, the most racist elements of the law were never enforced. It wasn't uncommon for white fathers to acknowledge black children, and help them acquire property and wealth. However, the late 18th century saw a strengthening of the racist elements in Saint Domingue. Free men of color were losing the rights to use honorifics, new laws about disrespect towards white people were being enforced, free people of color were banned from dancehalls, etc.

So to answer (part of) your question, it would have been not at all uncommon for a free person of color to have substantial wealth, although their prestige would be under attack in Saint Domingue. That said, the fact that Free people of color preferred to stay and acquire wealth in Saint Domingue rather than return to France suggests that such opportunities would not be available in France proper.

The Rising Economic Power of Free People of Color in the 1780s , John D Garrigus

Motion in the System: Coffee, Color, and Slavery in Eighteenth-Century Saint-Domingue, Michel-Rolph Trouillot

Colour, class and identity on the eve of the Haitian revolution: Saint‐Domingue's free coloured elite as colons américains, John D Garrigus