The fire comes days after 10 people were killed in a blaze at a Paris apartment building and a month after a massive gas explosion in the centre of the capital that left four dead in a building that also housed a bakery.
The Lyon fire broke out Saturday night after the blast in the bakery on the ground floor of the two-storey building.
“Two bodies were found, that of a woman and a child,” Lyon's public prosecutor Nicolas Jacquet said, adding that police were investigating the cause of the blaze.
Witnesses told AFP that a man who suffered minor injuries after jumping from the second floor told the fire service that his pregnant wife and child were still inside. Three passersby were also slightly hurt.
“Blue flames several metres high rose up from the bakery and engulfed the upper floors,” Chahine Reghi, a man living across the street, told AFP.
Tuesday's inferno in Paris was started by a resident with psychological problems, investigators said. The suspect, who is in her 40s, has been charged over the fire, which was the deadliest in the city in over a decade.