Leonarda Dibrani was removed from her school bus this month and deported from France, along with her her parents and five siblings, after they lost a battle for asylum, the BBC reported Saturday.
The family, which arrived in France from Kosovo five years ago, was flown back to Kosovo Oct. 8.
The case sparked demonstrations by student groups across the country.
"If [Leonarda] makes a request, because of the circumstances, and because she wants to pursue her schooling in France, a welcome will be extended to her," Hollande said in a television interview.
The teenager would have to return to France alone, he said.
Leonarda immediately rejected the offer, saying she would not "abandon" her family, Radio France Internationale reported.