The teenager at the centre of the row, herself condemned the French president as 'having no heart' for suggesting she return without her family. Photograph: Rex Features

The French president, François Hollande, was widely criticised on Sunday for offering to allow a deported teenage immigrant back into France without her family.

Hollande waded into the row on Saturday when he offered Leonarda Dibrani, a 15-year-old of Roma origin who was ordered off a school bus and deported to Kosovo, the chance to return to France to finish her studies, but only if she did so alone.

The proposal drew angry condemnation, including from Leonarda, who said she would not return alone, exposing Hollande to fresh attacks on his leadership.

"What do 80% of the French think about this?" asked François Bayrou, who ran against Hollande in the first round of the 2012 presidential election, on the digital news channel iTele. "They think the state has totally lost its compass, deciding one thing and then deciding its exact opposite one minute later … Hollande's authority is significantly weakened here."

Leonarda's expulsion after her family failed to obtain political asylum has tested Hollande's ability to handle the issue of illegal migration, a source of increasing public frustration in France.

Students protested to demand the schoolgirl be allowed back, but opinion polls showed that most French did not want the family to return. Opponents from the centre-right UMP party accused Hollande of being so obsessed with satisfying his Socialist base that he had betrayed the will of the public. Even members of his own party appeared dissatisfied with the president's attempt at a compromise.

Minutes after Hollande's TV appearance, in which he said police had followed rules but lacked tact in doing so, the Socialist party leader, Harlem Désir, appeared on a different channel saying Leonarda's family should be let back into France.

"I am going to talk to the president and the government about this," he said, adding that he wanted "all the children of Leonarda's family to be able to finish their studies in France, accompanied by their mother".

The Dibrani family suffered a further crisis on Sunday when Leonarda's mother Dzemila Dibrani was beaten and briefly treated in hospital in Kosovo.

She and Leonarda's father Resat Dibrani were accosted by another Roma couple in downtown Mitrovica, and she sustained unspecified injuries when the Roma man inquired about the fate of a child from their past romance, a Kosovo official said on condition of anonymity. Both couples are being questioned by police.

A poll in the weekly JDD newspaper showed Hollande's approval rating had sunk to 23%, the lowest level in his presidency and beating record low popularity ratings set by his predecessor Nicolas Sarkozy.

But while Hollande wilts under grim economic data and attacks on his authority, his tough-talking interior minister, Manuel Valls, has become France's most popular minister.

A JDD poll published this month showed Valls had the support of 61% of the public, far ahead of any other minister. By emphasising a tough stance on Leonarda's family rather than the offer to allow her back, he appears to have come out of the affair unscathed.

"Nothing will make me deviate from my path," Valls told JDD in an interview published on Sunday. "The law must be applied and this family must not come back to France."

Valls has toughened his rhetoric against illegal migration and makeshift Roma camps as the far-right National Front party has surged in popularity ahead of municipal and European elections next year.

Leonarda, who was born in Italy, and her five brothers and sisters attended school in France, where they arrived in 2009. But an official report showed their attendance record was patchy and said the family's attempts to assimilate were disappointing.

Repeated requests for asylum by her father, Reshat, who is from Kosovo, were undermined by the fact that he lied about their nationality.

Leonarda, speaking in French from a house in the Kosovo city of Mitrovica, criticised Hollande as "having no heart" and said her family would return to France anyway.