Notwithstanding the obvious error of classifying all black people as a race (Australian Aborigines and Saharan Touaregs for example are rather different) and ignoring the difficulty of using race to categorise people (as explained here) I'll take this as referring Napoleon's attitude towards ethnic minorities. In my opinion the clearest example of Napoleon's beliefs is that of Alexandre Dumas' father, General Thomas-Alexandre Dumas, who served in the French Army including a time under Napoleon. Note that much of Dumas' success owes itself to the culture of the Revolutionary Army which Napoleon embodied.

General Dumas was the product of a relationship between a French colonial nobleman and a slave in what is now Haiti. Technically this made him a slave, but when his father took him to France, where slavery was illegal, he became a free man. His father's aristocratic links enabled him to gain an education and join the French military. The pre-revolution military required proof of aristocratic descent for a commission which was not a problem for Dumas, but there were still racist laws in France which made it difficult for him to claim a title. In the end he enlisted as a private in the Queen's Dragoons as he was an exceptional horseman.

In the post-revolutionary France the notions of Liberte, Fraternite, Egalite (Liberty, Equality, Brotherhood/friendship) attempted to do away with social and class division and this extended across government and into the military which saw itself as a meritocracy. Thomas-Alexandre was offered a commission as a Lieutenant Colonel in a "Free Legion" of the French Revolutionary Army. He earned rapid promotion and by the age of 31 he was commanding the 50,000 strong French Army of the Alps.

Dumas served directly under Napoleon in the Army of Italy in 1796/7 and initially the relationship between the two men was strained. Dumas openly questioned some of Napoleon's policies, was given a command beneath his rank and was omitted from some dispatches. Whether this was solely due to his relationship with Napoleon or some underlying institutional racism is difficult to establish, but he was widely respected for his bravery and was head hunted by General Joubert so I suspect the former. This view is reinforced because after one particularly outstanding action at the Eisack River Dumas was personally rewarded with command of all the French cavalry forces in Italy.

Dumas' career was effectively ended when he was taken prisoner en route to Egypt after his ship was forced to dock in Taranto. In 1801, after 18 months in captivity, he was physically broken and incapable of resuming service. For some reason he was refused a General's pension and eventually died of stomach cancer in 1806.

There was a fantastic documentary on Thomas-Alexandre on BBC radio a while ago, I’ll see if I can dig it out.