Wimbledon champion Murray is still struggling with the elbow injury that forced him to miss the Miami Open.
"Not having Andy in the side is obviously a big loss ...but most importantly we all wish him well for a speedy recovery back to full health and fitness," Smith said. "I know that he would really want to be here with the rest of the team."
The 2015 champions will instead rely on Dan Evans and Kyle Edmund, ranked 43 and 45 respectively, to contest the singles rubbers in the April 7 to 9 clash in Rouen.
Jamie Murray and Dominic Inglot are the doubles players.
While Murray's absence is a blow, he also sat out the World Group first round tie in Canada which Britain won.
"This is a team with significant Davis Cup experience now and these guys have all stepped up and delivered performances at the very top of the competition," Smith said.
The two nations are meeting for the second time in three years after Murray inspired Britain to a quarter-final victory at Queen's Club in London in 2015.
France captain Yannick Noah also named his side on Tuesday which was notable for the absence of the country's two highest-ranked players, Jo-Wilfried Tsonga and Gael Monfils, as well as world number 22 Richard Gasquet.
Tsonga is lacking match practise after missing Miami because of the birth of his first child while Monfils, left out of the first-round win over Japan by Noah, is nursing various injuries.
Monfils has been named as a standby.
Gasquet recently underwent appendix surgery.
Leading the French challenge in their eighth successive quarter-final appearance will be world number 15 Lucas Pouille with Gilles Simon and Nicolas Mahut the other singles options.
(Reporting by Martyn Herman; editing by John Stonestreet)
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