World amount 12 Borna Coric put Croatia 1-0 up after outplaying world number 40 Jeremy Chardy.
Coric remained in control to win 6-2 7-5 6-4 and broke serve in the game.
By choosing for Chardy for its opening singles rather than the highest-ranked player in his squad, Lucas Pouille france captain Yannick Noah sprang a surprise.
But the gamble backfired for the hosts that are bidding to get an win.
France will hope when he takes on world number seven Marin Cilic in the second singles game of Friday the tie cans level.