Master's studies in France and Greece (one year per country) plausibility
If your plan is to live in each country one year, you would be better off by doing a master course of 2 years in Greece (or France) and being one year exchange student with Erasmus program in France (or Greece).
As far as I know, you can be Erasmus student without scholarship (which means you will fund yourself through the abroad stay).
Bureaucracy can be complicated (transcript of exams must be translated, syllabus not matching, etcetc) but being under the umbrella of the Erasmus Programm will help you a lot.