Sentence structure with "une fois" in French seems to be missing a verb, as compared with English construction

Question

There is a sentence structure that is used in French that I continue to be challenged with. Can someone explain what is going on or what the rule is in French?

Here is the original sentence:

• Une fois la préparation des paiements terminée, chaque prestation le composant fait l’objet d’une mise à jour de ses données au dépôt Rentes.

Which for me translates to the nonsensical sentence in English:

• Once the preparation of the payments terminated, each benefit the component makes the object of an update of its data in the Rentes depot.

To my anglophone mind, there appears to be a verb missing. For example, I would tend to think of writing the sentence this way:

• Une fois la préparation des paiements est terminée, chaque prestation du composant fait l’objet d’une mise à jour de ses données au dépôt Rentes.

Which to me makes more (but perhaps not perfect) sense in English as:

• Once the preparation of the payments is terminated, each benefit of the component makes the object of an update of its data in the Rentes depot.

I note that both sentences are correct according to Antidote. My francophone friend assures me that the first is correct and the second, though acceptable by Antidote, is not really correct in their mind.

Do they mean the same thing? If not, what is the difference?

If so, what rule in French allows the verb "est" to be removed and the "de" of "du" to be not specified?

Or perhaps more general, can someone provide the parsing of this sentence structure in French to help me understand where the subject is, the verb, and the object?

Answer 1

The sentence is something like a latin absolute ablative. An equivalent form could be: une fois que la présentation des paiements est terminée, ...

https://fr.wikipedia.org/wiki/Ablatif_absolu?wprov=sfti1

I also think that the correct pronoun is “les” and not “le”

Answer 2

The sentence is possibly incorrect and fooled you. It probably should have used la composant, although we would need more context to be sure. With a feminine or a plural, you probably wouldn't have confused the pronoun/verb le/la/les composant (composing it, it being the preparation) with the article/noun le composant (the component):

...chaque prestation la composant fait l’objet...

...each benefit composing it (i.e. composing the preparation) makes...

Answer 3

In itself this sentence is not correct ; the pronoun « le » is masculine singular and there is no word in it that is masculine singular and that could be referred to by this pronoun, not « préparation », not « paiements » ; therefore, either the pronoun is erroneous and most likely it is « les », or there is something else that is being mentioned before this sentence and that is what the pronoun refers to. In case this latter possibility is not verifiable, then, most likely what is being referred to is « paiements », which is why I supposed above that « les » was the pronoun needed. (Les paiements sont composés de prestations.)

• Une fois la préparation des paiements terminée, chaque prestation les composant fait l’objet d’une mise à jour de ses données au dépôt Rentes.

In other words, this sentence is equivalent to the following.

• Une fois la préparation des paiements terminée, chaque prestation composant les paiements fait l’objet d’une mise à jour de ses données au dépôt Rentes.

Your second sentence is not correct.