I prefer the reference letter system over the personal references system popular in the US because the letter decouples you from former employers. They don't get calls every time you're in talks with a recruiter. The amount of information that's passed along is standardized (even if it's a weird standard, but see below) and better controlled. It's possible to request interim reports, and when doing it semi-regularly…
In France you have a certificate of employment, "that guy was employed from that date to that date, for this job, and he leaves with/without strings attached" (non-competes, etc.) No judgement of valor, no personal stuff, it confirms the dates, the name of the company and the job title (be careful if you have been promoted internally without your official title adjusted).
Sure, they also show how much you were being paid, but presumably you could wait until after a salary negotiation to hand these over.