Metz have sacked head coach Philippe Hinschberger as a consequence of a "catastrophic" start to the Ligue 1 season.
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Debutant Kylian Mbappe, Neymar and Edinson Cavani flexed their muscles as Paris St Germain romped to a 5-1 victory over 10-man Metz.
Philipp Wollscheid has left Stoke to join Ligue 1 side Metz on a three-year deal, the French club have announced.
Riviere, 27, moved to St James' Park from Monaco in July 2014.
Monaco set a new Ligue 1 record as a 1-0 win at Metz made them the first team to win 15 consecutive matches in the French top flight.
Rennes have signed winger Ismaila Sarr from Metz on a four-year deal.
The Cameroon midfielder has left Metz after two seasons for a new challenge in the Czech Republic.
Midfielder Blaise Matuidi rescued Paris Saint-Germain with a stoppage-time winner after the French champions had wasted a late two-goal away to Metz.
Monaco restored their three-point lead over Paris Saint-Germain at the summit of Ligue 1 after coming from behind to defeat Dijon 2-1.
Monaco extended their lead at the top of Ligue 1 as Radamel Falcao's second-half goal secured a 1-0 win at Angers.
Lyon tightened their grip on fourth place in Ligue 1 with a 3-0 win at Metz, a game where all the goals came in the second half.
Alexandre Lacazette's 24th league goal of the season helped Lyon win 3-0 at to Metz and end a long spell without a win away from home.
Lille and Marseille played out a lacklustre goalless draw in the Ligue 1 on Friday, while Metz beat Bastia.
A late penalty from Edinson Cavani gave PSG a 1-0 win over Nancy on Saturday to move them level on points atop Ligue 1 with both Monaco and Nice.
Metz will no longer be docked any points for the crowd incidents that damaged the hearing of Lyon goalkeeper Anthony Lopes.
Metz, who are currently just a place and a point above the French top-flight's relegation zone, will make their case in at federation headquarters.
Paris Saint-Germain moved into second place in Ligue 1 by thrashing Marseille 5-1, while Memphis Depay scored a brace in Lyon's rout of Metz.
Mario Balotelli was sent off for the third time this season in Ligue 1 as Nice leapfrogged Paris Saint-Germain into second place in the table.
Monaco manager Leonardo Jardim believes that beating Metz is the perfect preparation for their upcoming Champions League game with Manchester City.
Radamel Falcao added Monaco's other two goals as the prolific pacesetters restored their three-point advantage over Paris Saint-Germain.
Dimitri Payet and Memphis Depay scored as Marseille and Lyon cruised to victories in Ligue 1 action on Wednesday.
Dimitri Payet's Ligue 1 return ended in despair for Marseille as struggling Metz produced a shock 1-0 win.
Yassine Benzia scored twice against his old club as Lille won 2-1 at Lyon, with the hosts missing the chance to close up on the Ligue 1 leaders.