What does "masters 2 level" mean?
At least at the universities in Paris where I took courses, there is a strong distinction between the first and second master year. In the first year you still take general courses in a variety of topics, whereas in the second year you really specialise. Someone explained to me that this is a remnant of how it was a while ago: first 4 years of undergraduate (which is now 3 years of bachelor, then the first year of the master), then 4 years of graduate (second year of master and 3 years of PhD).

I know that some of my friends in physics had something which could be called a research position at the master 2 level, i.e. they were integrated in the research group, doing some type of research, whilst not yet being PhD students.

So no, it should not be a second master degree, it should mean that you are in the second year of your master.