Video of the rescue shows 22-year-old Mamoudou Gassama, who climbs up four floors of the house in just a few seconds to save the child and applaud the audience.
When the Paris Rescue Services arrived at the building, he had already taken the child to safety.
Gassama told CNN daughter BFM TV after the rescue that he had been in the neighborhood watching a football game in a local restaurant when he saw the tumult.
"I like children, I would have hated to see him hurt in front of me, I ran and looked for solutions to save him and thank god I scaled the front of the building to the balcony ", he said.
The video shows neighbors on an adjoining balcony
French President Emmanuel Macron joined a choir of French leaders who congratulated the young immigrant, BFM TV said.
The French leader invited him to the Elysee Palace on Monday to personally thank him.
Paris Mayor Anne Hidalgo said on her official Twitter on Sunday that she had called Gassama to thank him and congratulate the Malian immigrant bravery
"He explained to me that he was dating Mali a few months ago with the dream I responded that his heroic act is an example to all citizens, and that the city of Paris is becoming apparent in supporting his efforts to settle in France, "she wrote on Twitter.