Through the shattered front windows of the bar in Rouen melted stools and scorched liquor bottles were visible, as tearful mourners hugged each other and brought flowers to the scene of the tragedy.
Most of the dead were between 18-25 years old, with one person among the six injured still fighting for their lives. Authorities said the bar was crowded with young partygoers.
Prime Minister Manuel Valls expressed "deep sadness at the tragedy that claimed 13 young lives."
"There wasn't an explosion, it was candles used for a birthday party," a senior police official told AFP.
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The flames ignited the polystyrene ceiling of the basement room where the celebrations were taking place, putting off a toxic mix of gasses that poisoned the victims, police said.
The blaze started at around midnight at the Au Cuba Libre bar in the city centre, and the firemen were at the scene by 00:20 am (0350 IST).
"A fire broke out in a bar in the city centre of Rouen this evening, according to an initial investigation, 13 are dead and six are injured, and more than 50 firemen attended the scene," Interior Minister Bernard Cazeneuve said in a statement.
The blaze in Rouen was France's deadliest since September 2005 when an apartment building fire in the Paris suburb of L'Hay-les-Roses killed 18 people.
France has not seen such a high death toll in a night spot fire since a November 1970 blaze claimed the lives of 146 people, the majority of whom were their early 20s.
Jittery France is on edge after a series of recent attacks by Islamic State-affiliated jihadists, including the killing of a priest in nearby Saint-Etienne-du-Rouvray.