The French Football Federation sent home striker Nicolas Anelka after a foul-mouthed rant at team coach Raymond Domenech, and the French players, led by team captain Patrice Evra, refused to train in protest at the decision to expel the Chelsea forward.
Now Sarkozy has asked Mme Bachelot to intervene.
Je suis retourne: Nicolas Anelka arrives back at Heathrow after his World Cup expulsion
A whole new ball game: France president Nicolas Sarkozy wants Anelka-Gate sorted out by his government
She said: 'We are taking note of the indignation of the French people and.calling for dignity and responsibility.
'It's not yet the right time to take disciplinary action but that time will come very soon.'
Economy minister Christine Lagarde, who represented her country as a synchronised swimmer, added: 'I am appalled.
'I am appalled because I have worn the French national colours as you know, and when you wear the French national colours you have added responsibilities.
'The first (responsibility) is to be the best possible in sport, but also to be exemplary because you are watched.
'There are young children, young adolescents who practise the sport and look to you as an example.'
Meanwhile, Ivory Coast striker Didier Drogba has come out in support of Chelseateam-mate Anelka.
What did you say? France coach Raymond Domenech asks Nioolas Anelka to repeat his words
Drogba insisted: 'He has been a team-mate for two and a half years. Yes, I support him. I wish him good luck, it's a difficult time for him. He is very strong mentally, he's a competitor. I was surprised he was kicked out of the team.'
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