As a former professor of constitutional law, I can tell you that this is not an issue for Quebec since they have a law preventing institutions from receiving funding directly from the federal government, with the exception of funding bodies. That is good and it is clear that universities fall under provincial jurisdiction.
As to the francophone mission of francophone institutions, we suggest that you go ahead and intervene directly if necessary. You do that with the Consortium national de formation en santé, the national health training consortium, for instance.
You have to stop holding back. We saw that with what happened at Immigration, Refugees and Citizenship Canada. People said universities were under provincial jurisdiction, and we asked the minister to set the institutions apart.