Her colleague, French video journalist Stephan Villeneuve, and their Iraqi Kurdish interpreter, Bakhtiyar Haddad, died earlier this week in the same explosion.
The journalists were covering Iraqi Special Forces' operations as they close in on the last remaining areas held by the Islamic State of the Levant and Iraq (ISIL, also known as ISIS) group in Mosul.
The three of them 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.
French Culture Minister Francoise Nyssen paid tribute to a "great war correspondent", in a post on the ministerial Twitter account.
She was repatriated to France for treatment but she succumbed to her wounds, the ministry added.
Robert had undergone surgery in a Baghdad hospital before being evacuated to France, the statement said.
Emilie Raffoul, a producer who worked with Robert for 15 years, told the AFP news agency: "She was someone who was very determined. They offer their most honest condolences", the head of the news department said in a statement.
According to the latest estimate by Reporters without Borders, Robert was the 29th journalist to have been killed in Iraq since 2014.
"The word sadness is not enough to describe how we feel", he said.
The presidential palace of the Elysee announced Tuesday that it will deliver posthumously the order of the Legion of Honor to Villeneuve.