Others might be able to provide examples of where someone has obtained a permanent position in the state system without going through the concours, but I had always understood that this was impossible. My ex-wife is a state registered teacher, and she went through the concours system, first CAPES, then AGREG. Even with that, you generally don’t get to choose which school to work at, you are assigned to a region first and then a school, depending on your career points, availability of posts, and other family considerations (rapprochement de conjoint, nombre d’enfants, etc) which are decided by a selection committee (with members taken from the inspection académique, rectorat, and unions) and approved by the rectorat. Even titulaires sometimes get assigned to several schools as replacements when they first get transferred to a given area, giving them the status of TZR, titulaire en zone de remplacement, where the “zone” can cover the whole region, i.e. you could be sent to 3 different schools in 3 different locations within a given region and work part-time in all of them.
The hierarchy and bureaucracy involved in the state system of appointments is one reason why some teachers seek out private school employment, whereby you use your state qualification to try and get a job in a private school under contract with the state. My understanding of this is that once you joined the private teaching system, you lost your state registration status and could essentially never go back, i.e. you can’t switch from private to state education institutions and vice-versa on a whim. I don’t know whether this has become more flexible in recent years, although I would be surprised if it has, as there is a huge inertia in the state education system with regards to career mobility. Someone on here who is still a state teacher might be able to fill in the gaps/correct me where my knowledge is lacking.
EDIT : further information about becoming a state registered teacher in lycee or collège here