Mennel Ibtissem, who is of Syrian origin, won praise from The Voice judges for her version of the song in English and Arabic.
But she appeared in a head wrap, sparking a furore in far-right and hard-line secular circles, as well as criticism that it was not sober enough from some Islamists.
Her right-wing critics then unearthed some Facebook comments on the terror attacks in France in 2016.
After the Bastille Day truck attack in Nice, she wrote "Here we go, it's become a routine, an attack a week, and, as usual, the 'terrorist' takes his ID with him. It's true that when you're plotting something nasty you never forget to take your papers with you."
That was a reference to the fact that police quickly named the some perpetrators of preceding massacres, including the 2015 Paris attacks, through documents found on their bodies.
In another post, shortly after two jihadists slit the throat of a priest in a Normandy church, she wrote: "The real terrorists are our government."
Apology not enough
Ibtissem apologised for the remarks, saying that her family had been celebrating Bastille Day in Nice on the day of the attack and she was upset by the authorities' failure to prevent it.
But relatives of the Nice victims joined in the criticism and she withdrew from the contest on Friday.
"I never meant to hurt anyone and the mere thought that my remarks hurt others hurts me, so I have taken the decision to quit this adventure," she said in a Facebook video that has been viewed over 860,000 times.
The production company behind The Voice, ITV Studios France, said it hoped her withdrawal would "ease tensions".
Many of her fans have expressed disappointment, however, saying the row was a symptom of Islamoiphobia and racism.
"Poor France, which confuses mistakes of youth with the horrors of her enemy," teacher Saïd Benmouffek said in an op-ed in Libération newspaper.
"It's rare to see a veiled woman on TV in a big broadcast with a large audience and not talk about the banlieues [socially deprived suburbs] and terror attacks," comedian Kheiron tweeted. "It was too much for the racist part of our country."