Xavier Ménard, 17, wanted to call his new graphic design company Wellarc, which is a combination of the French words for web, language, logo, artistic and company.
He said his application was refused by Quebec's business registrar because it does not respect Quebec's French Language Charter.
In an email to Radio-Canada, Marie-Pierre Blier, with Revenue Quebec, said Wellarc is not a French word and the name contradicts article 67 of the charter.
Ménard said he appealed the initial rejection and was again denied.
Ménard's lawyer sent a letter to the registrar claiming it is within his client's rights to combine words.
Ménard said many of the names he would have chosen in French were already taken by other businesses and said Wellarc is a made-up word that works in French and English.
"They want to restrain entrepreneurship, creativity," he said.
"I find a it a bit strange because here in Quebec we have some problems with the debt, we have some problems with the unemployment rate with the teenagers," he said, suggesting the province should be more encouraging of new business ventures.
He said his company would help the economy and promote French.
"They want to allocate resources to stop entrepreneurs of my age having a great name for the company and promote French worldwide, with a good company name and a good business in Quebec," said Ménard.
Teen broadcasts case on YouTube
Ménard posted a video on YouTube criticizing the provincial government, saying that the rules go too far.
He said he does not oppose the French Language Charter.
"I understand the need to protect French," he said, adding he would still like the province to reconsider how it goes about enforcement.
Since posting the video, Ménard said he has heard from others who have had similar problems with the registrar.
About nine per cent of requests for business names are rejected in Quebec every year because they do not meet the guidelines of the charter, according to the registrar.
Ménard is not sure what his next step will be, but said he may appeal again.
"I want to do business and create jobs, that's the main purpose of it," he said.