A process for the manufacture of dialkyl furan-2,5-dicarboxylate (DAFD) vapor composition by feeding furan-2,5-dicarboxylic acid (“FDCA”) to an esterification reactor and in the presence of an alcohol compound such as methanol, conducting an esterification reaction to form an esterification vapor containing DAFD, unreacted alcohol compound, 5-(alkoxycarbonyl)furan-2-carboxylic acid (ACFC), and water, and continuously passing the esterification vapor through an ACFC condensing zone, that can be integral with the esterification reactor, in which at least a portion of the ACFC in the esterification vapor is converted to a liquid phase condensate, and continuously discharging the esterification vapor from the ACFC condensing zone as a DAFD vapor. There is also a DAFD vapor composition containing DAFD, water, unreacted alcohol, and by-products.