Langgaard was born on 12 May 1811 in Copenhagen, the son of watchmaker Jens Bartholomæus Langgaard (1782–1832) and Marie Christiane Harm(s) (1784–1822). His father had studied watch-making in Aalborg but moved to Copenhagen in 1806 where he became the manager and eventually owner of a large clock and instrument business. He went bankrupt in connection with the Danish state bankruptcy of 1813. The family then moved to first Berlin and later, Landsberg an der Warthe. After his father's death, Langgaard apprenticed as a watchmaker on Rugen and then moved to Copenhagen where he was employed in Urban Jürgensen. He also brought his younger siblings back to Copenhagen.