"We'd like nothing more than to adopt her," said the girl's foster mother, Malén Liewehr to the TT news agency.
However as no biological parent has been identified then it the adoption process is complicated.
"We have been told that it could be difficult," Liewehr said.
Malén Liewehr and her husband have two children of their own and a further three girls whom they foster.
The girl in question was placed with the family when she was four months old.
"She can't speak any French. She know no other "mum and dad" aside from my husband and I," Malén Liewehr said.
Sara Skog at Save the Children in Malmö is critical of the Migration Board's handling of the case.
"It is horrible that they can think this way. You can ask whichever expert you like, they all think this way," she said to TT.
Skog argued that the girl will suffer further trauma if she is sent to France to an unfamiliar environment.
"A two-year-old girl has no idea what is happening around her and why," she says, arguing that the Migration Board is ignoring the UN Convention on the Rights of the Child (CRC).
"That this would be in the child's best interests is completely absurd," she said.
The child's mother came to Sweden two years ago from Algeria. Twenty days after giving birth to the girl, the mother vanished without trace and she was left in the care of her mother's husband.
The man is suspected of having abused her, according to a report by Sveriges Television. After the girl was admitted to hospital with injuries, she was then placed in the care of the authorities and a foster home was found.
It has not been established if the mother remains alive and the Migration Board's decision to deport the girl has been appealed.
It is unclear where the mother's and the Migration Board's decision has been appealed to the Migration Court of girl's special representative Kerstin Nilsson.
The girl has French citizenship through her mother, who has however never lived in the country.
According to Magnus Rosenberg at the Swedish Migration Board the child's needs will be met in France and underlined that it is very unusual for citizens of other EU countries to be granted a residence permit.
"It is now the responsibility of the French authorities to take the girl," Rosenberg said.
Rosenberg declined to specify whether the girl and her mother had any further ties to France aside from their citizenship.