However, he clashed with midfielder Didier Ndong and Bordeaux have now confirmed that he will need surgery to fix the cut.
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Menez completed his transfer from AC Milan to the french club two days ago and had a horrifying debut for the club though his side enjoyed a win.
Menez was taken to a local hospital, where he underwent surgery.
Ndong was remorseful following the gruesome incident, apologising to Menez via a Lorient statement.
Sky Sports quotes Ndong as saying: “I offer my apologies to Jeremy Menez and Bordeaux following a totally unintentional accident, which had unfortunate consequences for the striker”.
Bordeaux were ahead 2-0 at half time as Diego Rolan netted their first and Brazilian youngster Malcolm got their second.
Menez has been capped 24 times at worldwide level but last played for France in 2013.
The former French global, who joined Bordeaux this summer from AC Milan, was helped off the pitch in the 77th minute of the pre-season friendly match against Lorient on Wednesday.
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“The downtime of Jeremy Menez will be dependent on the healing”, the statement continues.
