Frølich was born in Copenhagen, Denmark. His father was a wholesaler. He studied in Copenhagen under Christoffer Wilhelm Eckersberg, in Dresden under Eduard Julius Bendemann from 1843–1846 and in Paris under Thomas Couture from 1852–1853. Afterward he lived much in Rome and in Paris, where he constantly exhibited at the salons. In 1877 he was appointed professor at the Royal Danish Academy of Art, Copenhagen. His illustrations, especially of children's books, are known everywhere and are more important than his paintings. His daughter Edma Frølich was his favorite model when a baby and a child for his French albums with Pierre-Jules Hetzel.
He also furnished original etchings for Illustreret Danmarkshistorie for Folket (1853–55) by Adam Kristoffer Fabricius; Die Götter des Nordens (1845) and De tvende Kirketaarne (1844) by Adam Gottlob Oehlenschläger, and many other works. He painted a decoration in the Court of Appeals at Flensburg, Schleswig-Holstein, and in some public buildings of his native land.
Danish painter and tapestry artist Dagmar Olrik (1860–1932) and her assistants spent 18 years decorating a room in Copenhagen's City Hall with tapestries based on cartoons of Nordic mythology by Frølich.
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