Thank you for your question. I am sorry for the delay in answering, which is due to the fact that I am one of the few EU-qualified experts here, and do have a main activity.
To answer your questions:
1. If you have British and, respectively, Greek passports, you may come to France without a visa or entry formality, and you may establish yourselves there, under the only caveat that, in order to have proof of your residence and time spent in France, you should (although there is no obligation) apply for the registration card (carte UE) and then, after 5 years for the permanent residence card. The cards are very useful because they prove when you settled in France, and provide you with identity documents to use daily. Furthermore, particularly for you as a British citizen, given Brexit, the registration will be essential to prove your entitlement to whatever rights of Britons in the EU will be agreed during Brexit negotiations.
2. You are right to be confused, because you have a very odd situation. As EU citizens, normally you would be covered by the social and health security system of exchange at the European level (basically your EU country of origin would give you a form that you would submit to the French health system, and thus ensure continuity). However, you lived and worked in Canada for so many years, so you do not have an EU health system "to come from". Therefore, the EU rules would not apply to you.
However, it does not matter much anymore. Since 2016, there is a new system called "Puma" (Protection universelle maladie) whereby every adult settled in France can register immediately upon settlement (basically when you get your registration card) and start benefiting immediately from the system. You can find information on registration for the social security number and where exactly to register here (https://www.ameli.fr/assure/droits-demarches/principes/regles-immatriculation-assures) and about documentation here (https://www.ameli.fr/sites/default/files/Documents/5421/document/regles-immatriculation-assures_ministere-affaires-sociales.pdf). Note your situation would be to file with the "Caisse d'assurance maladie (CPAM)" of the place where you will take residence, as indicated on the registration card.
I hope my answer was useful and look forward to your rating, which is essential to my activity.
Dr I L Vlad