The agency said 14 children between the ages of one and five have fallen ill between February and May.
Six children with hemolytic uremic syndrome (HUS) were infected with the same strain of E. coli O26 and consumption of reblochon is documented.
For the eight other cases, two with symptoms of gastroenteritis and six with HUS, investigations are ongoing to determine if there is a link to the cheese.
Cheese was distributed to more than 20 countries but none have reported associated illnesses.
French authorities have confirmed an epidemiological link between the cases and consumption of raw milk reblochon produced at the Cruseilles (Haute-Savoie) site of Chabert.
The exact source of contamination has not been identified and no food isolates have tested positive for STEC/VTEC O26.
The initial announcement of the outbreak last month reported seven sick and six with HUS.
HUS is not common in France with between 100 and 160 cases reported each year.
The recall of cheese has also been extended from mid-May to include product manufactured at Cruseilles but transferred to another site of the company to be cut and packed.
Twenty batches of Demi-fromage AOP reblochon laitier 240g with code FR 74.289.050 CE with a date before 29-5-18 are affected.
They were sold at Lidl, Leclerc, Auchan and Intermarché under the brands Saveur de nos régions, Nos régions ont du talent and Chabert.
Another type of reblochon under the name ‘tartiflard’ was marketed locally.
All lots and dates of fromage de Savoie au lait cru 450g with codes FR 74.096.050 CE - FR 74.303.050 CE was also recalled.
They were marketed in several stores in the Savoie and Haute-Savoie departments.
Authorities said raw milk cheeses should not be eaten by young children as a precaution and other types such as processed and pasteurized milk cheeses should be preferred.