Short answer. Yes. Article 1358 of the Civil Code requires the cession of actions or rights proceeding from an act appearing in a public document to itself appear in a public document. Since your right originally came from a notarized document, your assignment of that right must also be executed in a public document.
What the law says
The following must appear in a public document
Civil Code, Article 1358 — What Must Be in a Public Document. Read the full provision →
What the law says
The cession of actions or rights proceeding from an act appearing in a public document.
Civil Code, Article 1358 — What Must Be in a Public Document. Read the full provision →
What the law says
The power to administer property, or any other power which has for its object an act appearing or which should appear in a public document, or should prejudice a third person
Civil Code, Article 1358 — What Must Be in a Public Document. Read the full provision →
The rule for assigning rights that came from a public document
Article 1358 lists specific acts that must appear in a public document, and your situation falls under one of them directly: the cession of actions or rights proceeding from an act appearing in a public document. Because your right originally came from a notarized document, which is a public document, the assignment of that right is itself one of the acts this article requires to be in a public document, not merely a signed private writing.
Why the source document's form carries over
Article 1358 opens by naming this a category on its own: the following must appear in a public document. The cession item is listed as one of a small set of specific acts singled out for this treatment, precisely because the right being transferred traces back to something that was itself formalized as a public document. The article ties the form required for the assignment to the form the underlying act already had.
This sits alongside other public-document requirements in the same article
The cession you are asking about is not the only category Article 1358 covers. It also requires a public document for, among others, the power to administer property, or any other power which has for its object an act appearing or which should appear in a public document, or should prejudice a third person. Real rights over immovable property and hereditary rights are covered as well. Your assignment falls specifically under the cession category, not these others, but they share the same underlying pattern.
What this means for your assignment
Because the right you are transferring proceeds from an act that appears in a public document, Article 1358 places your assignment itself within the category of acts that must appear in a public document. Executing the assignment as a private writing would not satisfy what this specific item of the article requires, whatever the value of the right being transferred.