Assistant coach Arnaud Vercruysse will have sole charge of the team.
Club skipper and French international scrum-half Pierre Mignoni said: "A meeting was held and as players we slightly expected this. But it was solely Eric's choice. He was not pushed out by players or by the club.
"We must now come back with a good reaction on the pitch and act positively. It is the perfect match for us to show our commitment, but pitch conditions could be difficult."
Club president Olivier Nicollin said: "I have accepted Eric's resignation as coach, but he will still be with the club in charge of recruitment."
New coach Vercruysse was upbeat, saying: "A win in Neath and then a further big home win could still see us through and despite injuries it will still be 15 against 15.
"We must show a good attitude, but Neath did well against Cardiff last week and it will be difficult. They have a good pack and good half backs. The pack is heavy and dynamic."
Beziers: S Bonetti; P Escalle, J-M Aue, J-P Grandclaude, T Dejardin; G Quesada, P Mignoni (capt);S Chobet, D Swarzewski, S Bonnorino, K Ghezal, V Nadiradze, F Martinez, A Gardiner, F Gommard.
Replacements: J Selva, T Ratianidze, M Keita, R Castel, A Bousquet, Y Lafforgue, J Laharrague.