Slavery was pretty widespread in Europe until the late Middle Ages, including Christians enslaving other Christians and selling them to slave traders. 10% of the census population of the Domesday Book were slaves, not serfs. This changed when a pope (I can't remember his name off the top of my head) was concerned that Christian slaves owned by Jewish and Muslim slave-owners would convert to their masters' religions. That was just a prohibition against enslaving fellow Christians and selling slaves to Jewish and Muslim slave-traders though.

Yes to slavery being widespread in Europe of the dark ages. The church had something to do with its demise but I'm not sure it's one papal edict. Economics too.

But if "late Middle Ages" means say the time of the black death, and after, then at least in Western Europe that's much too late. By then slavery in England is long gone (or so rare as not to matter) and serfdom is in steep decline, and we are still several centuries away from European overseas slavery (no sugar islands before Columbus!)

Slavery in the islamic world was (I think) pretty continuous from the beginning until the 20th C. (Perhaps with ups and downs? There were many violent changes of leadership, over the centuries.) In the middle ages this would have been the primary meaning of slavery to Europeans -- the risk of being caught in some coastal raid and sold for labor (or for ransom, if noble). This no doubt horrified the pope but he had little power to stop this.