Robert had been operated on in Baghdad and then flown back for treatment in France overnight Thursday to Friday, but died of her wounds, the public broadcaster said in a statement.
French colleague Stephan Villeneuve and Iraqi Kurdish reporter Bakhtiyar Addad were also killed in Monday's blast.
All three were working for production company #5 Bis Productions on a programme for the French news programme Envoye Special, aired on public television channel France 2.
A fourth journalist with them, Samuel Forey, suffered light injuries.
Robert, 54, was an experienced war correspondent specialising in coverage of the Middle East, Iraq in particular, said the statement from France Televisions.
They were accompanying Iraqi special forces during the battle for the city, where jihadists from the Islamic State group entrenched in the narrow streets of the old town have set numerous booby traps.
France Televisions and #5 Bis Productions paid tribute to Robert's work and offered their condolences to her family in the statement.
Her producer Nicolas Jaillard wrote in a Facebook post that they had been hoping for better news. "The word sadness is not enough to describe how we feel," he added.
Reporters without Borders (RSF), the Paris-based media rights watchdog, also saluted her.
In comments on his Twitter account RSF secretary-general Christophe Deloire lamented the fact that too many foreign correspondents were being killed on the front line.
According to RSF's own tally, her death brings to 29 the number of journalists killed in Iraq since 2014.
On Tuesday, the French president's office announced that Villeneuve would be posthumously awarded the knight of the Legion of Honour, one of France's highest honours.