Valerie Begue has been told she should immediately take off her Miss France crown because of suggestive pictures published by a French magazine.
Valerie Begue in happier times with the president of the competition
Ms Begue - who became Miss France less than a fortnight ago - refused to resign, saying she had been betrayed.
She had returned on Thursday to an enthusiastic welcome on the Indian Ocean island of Reunion.
Before the competition, contestants guarantee that they have never been photographed in compromising positions.
One of the pictures shows her licking yoghurt provocatively, while another has her floating on a wooden cross in a swimming pool.
The President of the Miss France contest, Genevieve de Fontenay, went on French radio to insist that Valerie Begue would have to stand down.
If she did not, Ms de Fontenay said she would be stripped of her crown.
"She is in Reunion. Well, let her stay there," she said.
She went on to say that if she had been aware of the pictures, Ms Begue "would never have been let into the Miss France competition".
"I wouldn't want to be seen touring the provinces with a girl like that," she said.
After the contest organiser's comments were broadcast in Reunion, radio listeners expressed their shock.
It was the first time since 1978 that anyone from the island had been named Miss France.
And the honour came after a series of setbacks in Reunion including a tropical cyclone.
Hundreds of fans had converged on the airport to mark what newspapers described as the return of a princess.
At a news conference late on Friday, Valerie Begue told reporters that she would have some time for reflection before making a final decision.
If she does stand down, her title will be awarded to a runner-up.
The competition ran into similar controversy in 2005 when the then Miss France was stripped of her crown for posing for Playboy.