As a French colonial historian I only really feel comfortable referring to the French case.

First of all from the Enlightenment onward we see a shift towards scientific racism which eventually cements itself in Western thought lending credence to notions such as Kipling's "the White Man's Burden" which plays into the Scramble for Africa which you mention.

Post-French revolution we actually see an emancipation of slavery throughout the French colonies, which affects the Antilles in particular. This leads to many former slaves joining the republic, serving in the colonial army, as corsairs and even in government with Jean-Baptiste Belley from what is now Haiti being the first deputy of colour in the French national assembly. Sadly this legislative equality didn't really translate into full rights in many cases and even worse, when Napoleon formed the French Empire a few years later he rescinded the emancipation decree confining coloured people to slavery in the French Caribbean once again. This led to the Haitian revolution which resulted in the creation of Haiti as a free nation. In the other areas of the Antilles such as Martinique, Guadeloupe and Guiana, coloured people were eventually granted citizenship again in 1848 under the short-lived Second Republic. Coloured people did however continue to suffer from racism as well as from a substantial economic gap which led many to remain as workers on the plantations upon which they had been enslaved.

As for Africa, the degrees of racism varied depending on the colonial powers which ruled them. While all were racist, Leopold definitely set the bar for despotic insanity. Once again, in the French case we had a strange dynamic whereby colonies were formed and there was significant tension between Republican values which theoretically argued for equality and assimilation and right-wing values which encouraged bleeding a more hierarchical and racist system. The French colonies thus form a very strange example of colonialism whereby some colonial governors and administrators of African colonies were coloured themselves such as Félix Éboué who hailed from Guiana and worked in the colonial service in the first half of the 20th century. Being from one of the "old colonies" Éboué was deemed to have been so successfully assimilated to French culture as to be able to serve as a colonial administrator, nor was he the only coloured person to fill such a position, though he did rise the highest at this time in the colonial hierarchy.

Other colonies like Senegal were partially integrated into France and thus had their own Deputies such as Blaise Diagne.

All in all, to answer your question more directly, the abolition of slavery applied largely to the slave trade where it could be policed and to areas where slaves were brought to and registered. Within Africa, forced labour was par for the course among most colonizers, it simply wasn't officially acknowledged as such.

Some Sources/Further Reading:

Dubois, Laurent. A Colony of Citizens: Revolution and Slave Emancipation in the French Caribbean, 1787-1804. Chapel Hill: University of North Carolina Press, 2004.

Jennings, Eric. Vichy in the Tropics: Pétain's National Revolution in Madagascar, Guadeloupe and Indochina, 1940-1944. Stanford: Stanford University Press, 2001.

Régent, Frédéric. Esclavage, Métissage, Liberté: La Révolution française à la Guadeloupe (1789-1802). Paris: Grasset, 2004.

Price, Richard. The Convict and the Colonel: A Story of Colonialism and Resistance in the Caribbean Boston: Beacon Press, 1998.

Weinstein, Brian. Eboué. Oxford University Press, 1972.