"Naturally this young man, if he is a chess champion, merits that his case be examined with the greatest attention," Fillon told France Inter radio when asked about the status of 11-year-old Fahim Alam.
Alam arrived illegally in France in October 2008 with his father and in 2010 was issued with an order to leave the country.
He was sheltered for a time by an immigrant help group and currently lodges with families from his chess club in the Paris suburb of Creteil.
Alam won the junior French championship last month and would be able to join the national team in tournaments abroad if he had valid travel documents, according to the French Chess Federation.
Federation official Jordi Lopez said that Alam had the right to join the national team because he met the criterion of being enrolled in a French school.