In 1798, he took drawing lessons from Gerdt Hardorff, then accompanied his friend, Philipp Otto Runge, to Copenhagen, where he continued his studies with Jens Juel.
He and Runge were both dissatisfied with the training at the official academies, so they and several other fellow students established their own "Privat-Akademie", to supplement the standard curriculum.
Eiffe made little progress there, depending largely on Runge's contacts to promote his works.
This led to a rift between them, with Runge accusing Eiffe of not having any true artistic ambition.
There, he gave painting and drawing lessons and received a few orders, but his financial situation remained precarious.