When we discuss the Atlantic Revolutions, we are talking about the following, in chronological order: the American Revolution (1765-1783, with the Declaration of Independence occurring in 1776), the French Revolution (1789), and the Haitian Uprising and Revolution led by Toussaint L'Ouverture (1791-1804).
Each revolution was particularly influenced by John Locke's ideas about the natural rights of man. According to Locke, the law of nature obliged human beings not to harm "the life, the liberty, health, limb, or goods of another.” Though American patriots and French revolutionaries applied this principle to their own well-beings and visions for a more ideal state, they failed to apply this principle to the Native Americans whom they conquered, and the Africans whom they kidnapped and enslaved.
There are darker aspects of the Enlightenment which sought to justify the enslavement and mistreatment of non-European peoples. For example, in his Essays and Treatises on Several Subjects, David Hume -- the most notorious "enlightened" bigot wrote the following:
I am apt to suspect the negroes, and in general all the other species of men (for there are four or five different kinds) to be naturally inferior to the whites. There never was a civilized nation of any other complexion than white, nor even any individual eminent either in action or speculation. No ingenious manufactures amongst them, no arts, no sciences. On the other hand, the most rude and barbarous of the whites, such as the ancient GERMANS, the present TARTARS, have still something eminent about them, in their valour, form of government, or some other particular. Such a uniform and constant difference could not happen, in so many countries and ages, if nature had not made an original distinction betwixt these breeds of men. Not to mention our colonies, there are NEGROE [sic] slaves dispersed all over EUROPE, of which none ever discovered any symptom of ingenuity; tho’ low people, without education, will start up amongst us, and distinguish themselves in every profession. In JAMAICA, indeed, they talk of one negroe [sic] as a man of parts and learning; but ’tis likely he is admired for very slender accomplishments, like a parrot, who speaks a few words plainly.
The pseudo-science of racism, to which Hume clearly subscribed, developed during the Enlightenment, led by the faulty research of the German anthropologist and comparative anatomist Johann Friedrich Blumenbach. Blumenbach divided mankind into five families: Caucasian, Mongolian, Malayan, Ethiopian, and American. He examined the skulls of members of each group, using his studies to determine what he believed to be the innate tendencies and intellectual capacities predominant among each. His ideas would lead to phrenology, a nineteenth-century pseudo-scientific craze in which skulls were measured to determine intelligence and character, only furthering stereotypes about non-white groups.
As we now know, key figures in the American Revolution, such as Thomas Jefferson, also embraced racist theories. He expresses such notions in his famous essay "Notes on Virginia." One could argue that he was susceptible to the faulty science of his time, or that he and like-minded Americans accepted such views to legitimize slavery and Manifest Destiny.
More positively, Montesquieu's idea for three branches of government also arose from the Enlightenment. In his work The Spirit of Laws, Montesquieu, a French lawyer and political philosopher, argued for the separation of powers -- executive, legislative, and judicial -- to be allocated to separate individuals who would act independently of the other branches.
The early success of the American colonies could be attributed to the adaptation of this system of government. Though the French and Haitian revolutionaries fought, respectively, for independence and the natural rights of man, they failed to set up a solid and stable system of government, leading to years of insurrection and violence.