The French public health body said Friday it could not confirm or deny that the child's death was linked to eating the cheese.
Reblochon, whose name comes from the word "reblocher", which means "to pinch a cow's udder again", is an unpasteurised cheese made in the French Alps.
The E.coli outbreak has been traced to a producer, Chabert, and a recall of the cheese was ordered on 14 May when six children were hospitalised after eating it.
Public Health France said in a statement that, as of 31 May, 14 children aged from one to five years old are part of the investigation but only the six are known to have consumed the cheese.
On Friday evening Chabert announced a recall of all its new Reblochon batches "as a precautionary measure".
Contamination from E.coli, which mostly occurs through food, is dangerous can lead to severe kidney failure in young children.
After the previous recall, French authorities urged parents not to let young children eat raw-milk cheese.