Thursday's draw also pits Jiri Vesely against Lucas Pouille on an indoor hard court in the eastern city of Trinec.
For Pouille, who reached the quarterfinals at Wimbledon, it will be a Davis Cup debut.
In Saturday's doubles, veteran Radek Stepanek will team up with Adam Pavlasek for the Czechs to face Wimbledon doubles champions Nicolas Mahut and Pierre-Hugues Herbert.
Reverse singles are on Sunday.
The winner of the best-of-five series will play the United States or Croatia in the semifinals in September.
France won the last encounter 4-1 in the 2014 semifinals.