The midfielder left Leeds United a third of the way into a three-year contract.
Leeds United allowed Madger Gomes to leave last year, 12 months after they signed him from Liverpool.
Leeds United sold the midfielder prior to their new manager's appointment.
Gomes worked with Beale at Liverpool, but has now joined Sochaux in France from Leeds.
Former Liverpool youngster Madger Gomes did not play a game in the Championship for Leeds United.
Leeds United looked to have pulled off a coup luring Madger Gomes to Elland Road but the Championship outfit have now sold him to Ligue 2 Sochaux.
The Leeds United midfielder had a disappointing first season at the club.
Leeds United's Under-23s travel to Sheffield United on Monday afternoon.
Madger Gomes has failed to appear for the Leeds first team since August.
The Leeds United youngster will hope to be involved this weekend.
Who is better right now? Manchester City's Premier League superstar Raheem Sterling or Liverpool's Egyptian King Mo Salah?
Tanguy Ndombele proved his worth in the Champions League with Lyon last season and now he will be hoping to replicate that form when he makes his European debut with Tottenham Hotspur on Wednesday night.
Fikayo Tomori made his Champions League debut for Frank Lampard's Blues but Rodrigo Moreno scored the winner at Stamford Bridge.
Liverpool lost 2-0 away at Napoli on Tuesday night.
Liverpool are currently five points clear at the top of the Premier League table, with Manchester City's injury crisis worsening.
Liverpool and Chelsea are set to meet this weekend in Premier League action, with Jurgen Klopp's side facing defeat for the first time this term last night.
Arsenal trio are available and could all feature against Eintracht Frankfurt.
Tottenham Hotspur prospect Jack Roles has been rotated in and out of Cambridge United's side since being loaned out by Mauricio Pochettino.
Newcastle United and Manchester United were among the clubs linked with a move for Ansu Fati in the summer.
Leif Davis is lightning-quick, according to one of his Leeds United team-mates.