Mr Gassama is said to have arrived in France a year ago, taking the long and unsafe journey to Europe via a boat over the Mediterranean to Italy.
Accustomed to keeping his head down and staying out of trouble, Gassama said he didn't think of his legal status when he sprang to action. 'I climbed... Thank God I saved him'. God "helped me", he said.
"I had the pleasure to talk with him today by phone, to thank him warmly".
The video went viral and Gassama, who has been nicknamed "Spider-Man" for reaching the boy in the nick of time, was swiftly granted a meeting at the Elysee Palace.
"We'll obviously be setting all your papers straight and if you wish it, we will start the process of naturalization so that you can become French", he added.
A Malian migrant who saved a four-year-old child hanging from a fourth-floor Paris balcony after scaling the building with his bare hands was honored by French President Emmanuel Macron on Monday and offered citizenship.
A man in the neighboring balcony was attempting to hold the child up before Gassama reached out with his right arm and pulled the child to safety.
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French minister and former government spokesman Christophe Castaner also took to Twitter to say how admirable it was that Gassama stepped forward to save a life without giving any thought for his own.
And it turned Gassama into a national hero in France, where he was living illegally.
The child's father apparently left the child in the apartment alone to go shopping and play Pokemon Go.
Working as a firefighter corresponds with his skills, Macron said, and opened the door for him to join.
The boy's mother was not home either, Molins said, because she was visiting France's Réunion Island, in the Indian Ocean, with family members.
The father of the toddler has been questioned by police on suspicion of leaving his child unattended, according to Parisian judicial sources.
The father, who was arrested on charges of neglecting his parental duties, was released from custody and reunited with his son on Monday under the supervision of social services.