Was the use of African slaves common in Europe itself, or was it mostly limited to their colonies? Would a French noble on the eve of the Revolution have black slaves in his chateau? What about the wealthier members of the Third Estate?
Slavery was not common in Europe in the late 18th century.
It had been abolished in Iceland in 1117. The Magna Carta in England (of 1215) was interpreted by the courts (clause 30) as banning slavery in England. The town of Bologna in Italy abolished slavery in 1256. By 1274, slavery was abolished in Norway. In 1315, Louis X abolished slavery in France (though it continued in some degree in the South of France, along the Mediterranean until the 17th century. In 1335 Sweden made slavery illegal. In 1347 Poland abolished slavery. In 1588 Lithuania abolished slavery. In 1723, Russia abolished slavery. In 1761 Portugal abolished slavery in Portugal and Portuguese India.
So, there was almost no slavery (legally) in Europe by the late 18th century. There were some places where it had not been made illegal (Ireland, Scotland) but rarely existed. It was also not present in Germany, the low countries, Switzerland, and much of Italy, but the fragmentation of jurisdictions in those places means that tracking the dates of abolition would be complex.
French nobles would not have had slaves (in France. They might have had them in the French Caribbean, if they owned plantations there.). When Thomas Jefferson brought his slave and mistress, Sally Hemings, to France when he was US ambassador, he and she were both aware that she was free in France. He apparently persuaded her to remain a slave and return to the US with him through a promise to free their children (which he did).
I think slavery was still legal in Spain. But I don't think there were large numbers of slaves there.
The main slavery in Europe by the late 18th century was in the Ottoman Empire, where slavery was still practiced. The other exception was the Crimean Tartars. They made their last major slave raid into Russia in 1769, and held slaves until conquered by the Russians in 1783. There may have still been slavery in the Caucasus.
The Barbary States, in North Africa, were also still seizing European ships and enslaving the crews and raiding European coastlines for slaves in the late 18th century.