Yes, absolutely. During the negotiations on the agreement between Canada and the European Union, it was said that Quebec would participate. However, Pierre Marc Johnson, who was the chief negotiator at the time, said that Quebec's participation was more in the hallways than at the negotiation table.
Given the importance of the sectors for which the provinces are responsible, such as health, education and culture, and the fact that they can be negotiated in free trade agreements, I think there should be more room for the provinces in the negotiations for free trade agreements.