Franke is a product of Dynamo Dresden's youth setup, and was promoted to the first team in 2010. He made his debut in March 2011, when he replaced Sascha Pfeffer in a 3. Liga match against SV Wehen Wiesbaden. In Summer 2013 he was signed for Hallescher FC by former Dynamo Dresden coach Sven Köhler.
In July 2017, he signed for Norwich City on a three-year contract, for an undisclosed fee.