His mother was out of town.
Paris public prosecutor Francois Molins told news site 20 Minutes that the father, a man in his thirties, "got it into his head" to play the game after shopping and was "distraught" to learn what had taken place in his absence.
His actions went viral on social media, where he was dubbed "Spiderman".
Gassama is an immigrant who arrived from Mali just a few months ago. "I climbed up like that and, thank God, I saved the child", 22-year-old Gassama told reporters the day after the incident, according to The Guardian.
President Emmanuel Macron personally thanked him, gave him a medal for courage and said he would also be offered a role in the fire service.More news: Starbucks to close over 8000 stores for employee anti-bias training
More news: 'Murdered' journalist Arkady Babchenko turns out to be alive
More news: Canadian government to buy troubled Trans Mountain pipeline
Mr Gassama told Mr Macron he was arrested and beaten during his long, rough stay in Libya "but I wasn't discouraged". I felt afraid when I saved the child.
Meanwhile, his 4-year-old son had slipped off the balcony and dangled precariously off the side of their building by his hands. By Monday, Gassama was meeting face-to-face with Macron and received recognition for courage, approval for French citizenship and a job as a firefighter. "I replied that his heroic act is an example for all citizens and that the city of Paris will obviously be keen to support him in his efforts to settle in France", she posted to Twitter.
Mr Gassama has been hailed a hero and has been offered French citizenship.
The father of the child was detained overnight for alleged parental neglect, and is to appear in court in September.
A couple in the neighbouring apartment, located in Paris' 18th Arrondissement, were trying to reach the child but were unable to safely lift the boy over to their side.
"I did it because it was a child", French newspaper Le Parisien quoted the 22-year-old as saying. "When we realized the child was safe we all started clapping and congratulating him because what he did... honestly... it was unbelievable", explained eyewitness Cissokho Goundo.