1) you can only get promoted if the company grows and/or someone above you leaves, or dies, or ... Btw it really requires leaving permanently. They leave for 10 years due to being in coma after a traffic accident? Nope.
2) the oldest person gets promoted (and that means ancienneté: longest in the company). No arguments, no exceptions. To the point that there are plenty of teams that have a manager (who gets the 10% pay boost) and an actual manager (who makes things work). Often not the same person.
3) No mobility (technically, yes, there's mobility, BUT your ancienneté resets in many cases. So it's really stupid to do)
Credit Agricole, a "cooperative" bank that is ruled by union contracts that impose strict limits on how many commas in the rulebook are allowed to move per decade. A company where any change gets so stuck committees they found it easier to implement changes through parliament than through the company's own management structure. Several times.
Total, government owned oil company that gets special tax treatment and gives free shares to French presidents and ministers who leave office. Actually has a good reputation as an employer, but not because there is any chance in hell of getting promoted.
EDF, the power company (mostly nuclear), who are positively famous in how difficult they are to work with, both internally and externally. But, have a good reputation as an employer.
France Telecom, which used to be a subsidiary of EDF. They split off to remove worker protections from their (many) employees. Still extremely tied to the government. They have an extremely poor reputation as an employer (as in they have driven employees to suicide).
If you try to start any such companies in France, the government is going to outright sabotage you, whatever the laws say.
They are often both illegal and unenforced. Your old employer isn't going to waste time hiring a private detective to track down every former employee's new work place that you didn't include on LinkedIn.