Ah, French law. How to explain what un témoin assisté is, and why the director of the IMF is one as of today? In the old days, a "person of interest" in a criminal case could either be a "witness" (témoin) or "indicted" (inculpé). In 1987, however, the law was changed: one was no longer indicted but rather "mis en examen," that is, placed under official investigation. Short of that, but somewhere this side of exonerated, was created the new status of témoin assisté, no longer a simple witness but not exactly an accused. Presumably this was meant to preserve the "presumption of innocence," thought to be somewhat compromised by indictment or its more modern counterpart, which suggests at least a preliminary belief in the person's involvement in the commission of some crime.
The témoin assisté has certain rights, including the right to have an attorney examine the case files and appear with the witness, to insist on confrontation with accusers, and so on.
To a simple-minded Anglo-Saxon, it all seems rather a muddle, and for now it probably won't affect Lagarde's IMF position. The Fund has declared its confidence in her and knew about the allegations when it hired her. But it also declared its confidence in DSK before dumping him--not that the cases are in any way comparable.
I suspect that Lagarde, as a veteran litigator in the US, will plead that the use of a panel of private arbitrators to settle a complex lawsuit involving teams of corporate lawyers on both sides was a perfectly reasonable way to proceed and far more likely to be fair and efficient than a jury trial. How was she to know that there would be reason to doubt the neutrality of the arbitrators? Or whatever.
There will be so much smoke blown here and there before this case is over that I doubt anyone will know what happened in the end. And who really cares whether the bankers diddled Tapie or Tapie the bankers? The state should have gotten more out of the deal, but in the grand scheme of things, it's a pittance. Anyone who can say what Justice is in this case has more patience than I have. But resonant words will be spoken, no doubt, and grand claims advanced, and in the end there will be a settlement, and perhaps someone will go to jail. But I doubt it will be Christine Lagarde.