My daughter is a Canadian citizen/resident who also has a UK/EU passport. She's going to study in France for 4 months next January. Can she obtain a European Health Insurance Card and if so, how would she apply for it? I looked at the EHIC application form on the UK NHS website and it says she must be ordinarily a UK resident to use that form. Obviously that is not the case as she resides in Canada so I don't know which channels she should apply through.
To get a European Health Insurance Card, you need to be covered by a statutory health care/health insurance system in one of the participating countries. In the UK, it basically means being a resident. Citizenship is not relevant, non-citizens can have access to the NHS and get an EHIC if they reside in the UK. But British citizens are not automatically entitled to one if they don't.
Without EHIC and since she is a student, she might be eligible for statutory health insurance (sécurité sociale étudiante) instead. It's not very expensive (€215 for a full year) so it could be an easy solution.
It's also possible that there is a reciprocity agreement with your insurance in Canada (there is one with Québec for example) that would work a bit like the EHIC system. You might want to look into that.