Spaniard Verdasco was leading first-round opponent Robin Haase 6-2 3-2 in Paris when the Dutchman retired with a hip injury and he will now face Murray, one of 16 seeded players handed byes into the second round.
Murray edged a step closer to overtaking Novak Djokovic at the top of the world rankings by winning his third successive title at the Erste Bank Open in Vienna on Sunday, beating Frenchman Jo-Wilfried Tsonga 6-3 7-6 (8/6) in the final.
Murray can become world No 1 for the first time in his career if he wins the Paris title and Djokovic fails to reach the final.
A final appearance for Murray, who also won titles in Beijing and Shanghai earlier this month, would also be good enough if Djokovic fails to reach the last four.
Pablo Carreno Busta eased to a 6-3 6-1 victory against Italian Fabio Fognini and will play fourth seed Milos Raonic in the second round.
Third seed Stan Wawrinka will play Jan-Lennard Struff in the second round after the German qualifier thrashed Ukraine’s Illya Marchenko 6-1 6-1 and Italy’s Paolo Lorenzi beat Benoit Paire 6-4 7-6 (7/4) to set up a meeting with Pablo Cuevas of Uruguay.