Heuer was born during the occupation of Hamburg by the Révolution françaises' army in Hamburg's Görttwiete near the Hopfenmarkt. He was the son of tailor's Johann Friedrich Heuer and Christina Magdalena, "née" Lehmann from Uelzen. His birth was registered in the French vital records of Hambourg under number 2738. When he was just one year old, his parents moved to a house in the Stavenpforte and later to the Altenwallstraße. The house there fell victim to the Great fire of Hamburg in 1842.