The former Arsenal and France midfielder was brought in to replace Lucien Favre after his departure for Borussia Dortmund, but his reign got off to a miserable start.
Moussa Doumbia scored the only goal of the game in just the second minute of his Ligue 1 debut after joining Reims from Russian side Rostov.
The Malian midfielder cut inside two defenders before beating Nice goalkeeper Yoan Cardinale at his near post with a low shot from long range.
Nice dominated the rest of the match -- enjoying 71 percent of possession -- but only one of their 19 shots on goal was on target as they missed the injured Mario Balotelli.
Visiting 'keeper Edouard Mendy was equal to a low effort from Allan Saint-Maximin, but Nice created little else as Reims clung on to mark their return to the top flight after winning the Ligue 2 title with an unlikely win.
Vieira, who had been briefly linked with the manager's job at Arsenal during the close-season, will take his new team to Caen next Saturday, as the 42-year-old looks for his first win since leaving New York City.
Falcao helps Monaco to winning start
Radamel Falcao came off the bench to score and set up another goal as Monaco brushed aside Nantes 3-1 to get their Ligue 1 campaign off to a strong start.
With Falcao left out of the starting XI following his World Cup exertions with Colombia and big summer signing Aleksandr Golovin out injured, Monaco struggled for long periods.
But the game changed when Falcao was introduced in the 66th minute, and Rony Lopes continued his excellent form from last season by stooping to nod in the opening goal just three minutes later.
Falcao set Stevan Jovetic free with 10 minutes to go, and the Montenegrin coolly slotted home.
Samuel Grandsir, who also came on with Falcao to make his Ligue 1 debut for the club, crossed low for the Colombian to tap into an empty net in the 83rd minute, as Monaco cruised to victory despite Emiliano Sala's injury-time consolation.
"We still have a lot to improve, but this victory is good to start the season well," Portuguese youngster Lopes told Canal+.
"Last week (4-0 Champions Trophy loss to Paris Saint-Germain) was difficult, but here, first game of the championship, a win, we're happy."
Elsewhere, Nimes scored three goals in the last 14 minutes to grab a thrilling 4-3 victory at Angers in their first top-flight match since 1993.
Whabi Khazri scored on his debut as Saint-Etienne beat Dijon 2-1, while Lille came from behind to win 3-1 against Rennes and Montpellier lost at home to Dijon.
Reigning champions PSG get their title defence underway on Sunday when they host Caen.
Marseille opened the season in style on Friday night as Dimitri Payet scored twice in a 4-0 thrashing of Toulouse.