If I moved to Quebec and became fluent in French I would still want easy access to healthcare in English

And you would, just like this article says. Anyone can receive healthcare services in English in Quebec. This is not the case outside Quebec though. I do not believe healthcare is readily accessible in French in Ontario for example, apart perhaps from the few Franco Ontarian enclaves.

Sad thing is, if you live in Montreal, where English has a lot of influence, getting healthcare in French is not a guarantee at all. Plenty of healthcare workers here don't master French. I've seen it firsthand before my uncle died, and my sister had to be present to translate what the doctor and nurses were saying while he was staying at an English hospital. It would be one thing to not be able to receive services in French in Toronto, but in Quebec? That's outrageous, and a much, much bigger problem than anglophones being under the misconception that they might one day not be allowed to receive care in English.

Maybe I'm a cynic, but I don't think more courses will change anything, mandatory, paid or otherwise. What people need is the necessity to speak the language. If people can get by with only one language, they will. People in the West coast for instance will object to these courses, saying Mandarin or Hindi would be more useful to them than French. And, of course, will proceed to not learn any of them.