Providing a mixed service within a single institution presents challenges. You have to understand that, in a minority setting, the majority language prevails. In an institution that offers both services, the majority language would prevail, and it would set the tone for the students' school environment. It is therefore very hard to provide quality service in French as a first language in a mixed environment.
However, compromises could be made. My experience is proof of that. The immersion school in my village had a gymnasium built for the francophone community with funding from Canadian Heritage. When I became a student at the francophone school, my access to the gymnasium was restricted because I wasn't part of the majority school board.
There was obviously a legal challenge, and we won. I was able to access the gym. Afterwards, a French school was built in my village. Both schools had access to the gymnasium and science lab. The buildings were separate, but we were allowed access to some parts of the infrastructure.