The children, the youngest of whom is 20 months old, had eaten defrosted hamburgers made by the French company SEB which said the meat was provided by several suppliers abroad and processed in France.
The "Steak Country" burgers were bought in French branches of German-owned supermarket Lidl. SEB said it had recalled them and Lidl said it had removed them from its shelves in France.
Health authorities said the infection was a rare strain of the E coli bacteria and was not linked to the outbreak in Germany.
The children suffered from bloody diarrhoea, which also struck victims of the outbreak in Germany which has been blamed on infected vegetable sprouts.
The French infections "have no link at present with the recent epidemic in Germany," a health official said. But tests took place on Thursday morning to ensure that this is the case.
Thechildren come from different towns and SEB boss Guy Lamorlette said that one of them claimed not to have eaten hamburger.