Kagome networks of ferromagnetically or antiferromagnetically coupled S = ¹/₂ magnetic moments represent important models in the pursuit of a diverse array of novel quantum and topological states of matter. Here, we explore a family of Cu²⁺-containing metal-organic frameworks (MOFs) bearing S = ¹/₂ kagome layers pillared by ditopic organic linkers with the general formula Cu₃(CO₃)₂(x)₃·2ClO₄ (MOF-x), where x is 1,2-bis(4-pyridyl)ethane (bpe), 1,2-bis(4-pyridyl)ethylene (bpy), or 4,4′-azopyridine (azpy). Despite more than a decade of investigation, the nature of the magnetic exchange interactions in these materials remained unclear, meaning that whether the underlying magnetic model is that of an S = ¹/₂ kagome ferromagnet or antiferromagnet is unknown. Using single-crystal X-ray diffraction, we have developed a chemically intuitive crystal structure for this family of materials. Then, through a combination of magnetic susceptibility, powder neutron diffraction, and muon-spin spectroscopy measurements, we show that the magnetic ground state of this family consists of S = ¹/₂ ferromagnetic kagome layers that are coupled antiferromagnetically via their extended organic pillaring linkers.