Three questions on (finding) permanent positions in France
It's hard to give a general answer, but yes, they are more competitive. CNRS/INRIA positions are nationwide competitions (in the sense that a MCF is tied to a university, while a CR is tied to CNRS/INRIA which are national institutes, so a CR can request of change of assignment and move to another French university rather easily). They are also intrinsically more attractive than MCF positions: you get no teaching duties for the same salary, and you can still teach if you want to so long as the department has some teaching vacancies not filled by permanent teaching staff -- and they almost always do.
It is technically &quot;possible&quot; in the sense that there is no legal obstacle to it. The only way to do this is to get your MCF position, then apply like everyone else to a CR position when it opens. Maybe things are different in CS (I'm in math) but I do not know anyone who has managed to do it, or even expressed the desire to try. Recruiting committees know that giving a permanent position to a postdoc is life-changing, while giving a permanent position to someone who's already got one is only a change of assignment. They heavily lean towards the first.
Yes, it is possible. I have several colleagues who do it.

Just a note, the positions offered by the CNRS and the INRIA are the same, &quot;chargé de recherche&quot;, and have the same statutes. It's just a different employer. CNRS and INRIA are both the same kind of legal entity, an EPST.