The case, which was first brought to court in 2009, argues that the Yukon's French school board should have the right to determine who its students are.
Section 23 of the Charter of Rights and Freedoms guarantees Canadians the right to education in a minority language, whether English or French, but extends that right only to the children or grandchildren of those who were educated in that language or who learned it as their first language.
The Yukon government argued for the strictest interpretation of who should be allowed to attend minority language schools.
The territory's francophone school board argues there is a need to allow some exceptions in enrolments for immigrants and families who have lost their language over time.
Quebec, which sides with the Yukon government, worries that a broader interpretation of law could mean more students would be admitted to Quebec's English schools.
Pierre Foucher, a constitutional law expert and lawyer at the University of Ottawa, says Quebec's position does nothing for the relationship between it and francophone minorities in the rest of the country.
"It's like we've been abandoned," Foucher says.
In Whitehorse, the president of the francophone school board, Ludovic Gouaillier says he's disappointed in Quebec.
"It's a position that contradicts other statements that have been made by Quebec in the past about supporting the growth of francophone minorities outside Quebec," Gouaillier says.
Foucher says if francophone schools outside Quebec are allowed to make some exceptions to their enrolment, it will help minority communities grow.
"On the one hand they call themselves the centre of the French life in Canada and on the other hand they seem not to realize that there is a French life outside of Quebec also trying to survive, trying to improve their conditions and going to court for that," he says.
Foucher says Quebec took a similar position to B.C., Saskatchewan, Alberta and N.W.T. on minority language education.
"In the west and the north the attitude toward French language education tends to be restrictive, so to see Quebec argue exactly the same position is puzzling for the French minority."
AndréBourcier, a former president of the Yukon's francophone school board, says he understands Quebec needs to protect the French language but "to take a position to do so on the back of francophones elsewhere in Canada is difficult to understand," he says.
"They could have defended their position in a different way but they went basically to kill a fly with a sledgehammer."
The Supreme Court is likely to take at least six months to consider the case.