For background, an aveu judiciaire isn't called a "confession" in EN. That word is reserved for criminal matters (confessing to a murder, etc.). An aveu judiciaire can be a criminal matter, civil matter, family-court matter, etc. -- any legal issue that could possibly end up in court. In EN it is called a "judicial admission":
https://definitions.uslegal.com/j/judicial-admission/

The reference SafeTex posted is legit and useful, but his translation is meaningless. What that reference explains is that in FR law, when a party makes a judicial admission, in order for the judge to use that admission as the basis for deciding against the person who made the admission, the judge has to take the admission in its entirety, as a whole. They can't just take one part of it.

So (overly simplistic example) if someone admitted on the witness stand, "Yes, I illegally dumped my company's toxic chemicals in the Potomac River," but the trial is about illegally dumping chemicals in the Charles River, you can't use the first part of the admission as proof that the defendant dumped chemicals in the Charles River. You have to look at the entire admission -- and it's about a different river, so it's not proof that he dumped chemicals in the Charles River.

In EN legalese we talk a lot about things being used "in whole or in part." That actually means something that an EN lawyer/paralegal/other person likely to be reading this text would understand. So it works here: a judicial admission cannot be used only in part against its author. We understand that to mean that if you want to use it at all, you have to use the whole thing.







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Note added at 1 hr (2019-10-14 18:31:18 GMT)
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PS re your comment on SafeTex's suggestion: Yes, that's exactly what "contre son auteur" means: against the person who said it; as evidence against him; to the detriment of his case. And you can just translate it straightforwardly as "against its author."

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Note added at 23 hrs (2019-10-15 15:56:55 GMT)
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To address Adrian's totally misplaced concerns, I will make life easy by pasting the key points from the link that I already provided:

"Judicial admission means an admission made by a party in a judicial proceeding... or a failure to officially dispute an assertion. Judicial admissions must be in writing except when they are part of the court record" (i.e., when they're said in testimony, so they appear on the transcript). https://definitions.uslegal.com/j/judicial-admission/

So, Adrian:
(1) no, it has nothing to do with judges admitting evidence;

(2) yes, it's an in-court admission, as in the FR;

(3) no, it has nothing to do with judicial notice (https://dictionary.law.com/Default.aspx?selected=1065; and

"3(b)" (your numbering system) no, the word "author" doesn't imply that the admission is written rather than oral. For instance, a singer is the "author" of a copyrighted sound recording; see also definition 2a here: AUTHOR - "one that originates or creates something: source" (author of software; author of a film; author of a crime).
https://www.merriam-webster.com/dictionary/author