The 29-year-old rejoined Metz from AJ Auxerre two years ago despite contrasting fortunes for both clubs at the time, and went on to captain Les Grenats during their immediate return to the top flight.
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Hein produced strong individual numbers in Ligue 1 with eight goals and seven assists, but was unable to prevent Metz from suffering relegation back to Ligue 2 last season.
Nice, who narrowly avoided relegation themselves, are now restructuring under new manager Olivier Pantaloni and an incoming sporting director.