Fallesen was born in Copenhagen, the son of Lorentz Nikolai Fallesen, a Protestant clergyman and theologian. He studied at the University of Copenhagen and then at the Royal Military College. After receiving his commission as a First Lieutenant in 1846, he was appointed to the artillery corps of the Danish Army. Fallesen served in both the First and Second Schleswig War, eventually rising to the rank of Captain and serving as a member of the international commission that formulated the 1864 Treaty of Vienna. However, his health had suffered during the second Schleswig campaign, and he retired from active combat duty in 1865. His final military appointment was as Colonel of the Bornholm Regiment in 1866.