Philippe Landreau, the surgeon who carried out the operation, revealed Marconnet's injury was "complex" and expects the 30-year-old, capped 71 times for Les Bleus, to be out of action for five months.
With the World Cup beginning at the start of September, Marconnet faces a race against time to be fully fit for the showpiece, which is being held in his home country.
Landreau said: "The fracture was a big one, quite complex. Fortunately, it is not an open fracture.
"For a simple fracture, it is three months (out of action). After a fracture like this one, in order to have a proper strengthening of the bone, it is a minimum three months, but perhaps more."
Asked when the front-row forward would be back in training, Landreau added: "The start of the fifth month, not before. In this case, that leads us to the start of August.
"But to recover completely, it is six months. And six months - that is September 6, when France play Argentina. We have spoken to Sylvain about it and he has made his calculations.
"That Sylvain will have recovered in six months, I have no doubt. But what state will he be in?"