After matriculating from high school in 1920, Eickhoff embarked on law studies but changed paths in 1926 when he became a pupil of Harald Giersing.
Realizing he would now concentrate on sculpture, he continued his studies in Paris from 1927 to 1933 under Charles Despiau, associating with a wide range of sculptors including Jean Osouf and Paul Cornet from France, Charles Leplae from Belgium, Han Wezelaar from the Netherlands, Bror Hjorth from Sweden and Adam Fischer and Astrid Noack from Denmark.
His works from this period follow the French trends of Aristide Maillol and Charles Despiau, contrasting with Danish designs.
He frequently sketched during his travels, producing such prized works as a drawing of a cow deprived of its calf in San Cataldo (1952) and of a shop in Zauen, Morocco (1953).
They contrast with those of previous generations, differing from the exuberance of Kai Nielsen and the ornamentation of Johannes Bjerg and Einar Utzon-Frank.