A Berlin native and product of Eisbären Berlin, Köppchen spent the 1997-98 season in the Manitoba Junior Hockey League, playing for the Neepawa Natives. He made his debut in Germany's elite league DEL for the Munich Barons during the 2000-01 season. The Barons relocated to Hamburg in 2002 and became the Hamburg Freezers. Between 2004 and 2011, Köppchen played for the Hannover Scorpions and helped guide the team to the 2010 German championship. He returned to the Hamburg Freezers in 2011.
On 6 April 2013 Köppchen left the Freezers after two seasons and signed a one-year contract with ERC Ingolstadt.[2] Serving as a team captain, he won the German championship with ERC in 2014[3] and was named MVP of the playoffs.
He parted ways with ERC Ingolstadt in July 2017 and signed with fellow DEL club Nürnberg Ice Tigers.[4] Köppchen reached the playoff-semis with Nürnberg in the 2017–18 season, before in May 2018, he left and was signed as a free agent to a one-year deal with Düsseldorfer EG.[5]