I’m by no mean linguist, but being french I may be able to help.

I think to confess is a misleading translation, I can’t think of a sentence where it could be exactly used as such. The closest would be “Admettre ses erreurs” (To admit/accept/acknowledge your errors); which is more introspective than confessing.

A better example of “to give entree into your acknowledged awareness” would be the use of admettre to accept something as true:

“J’admets que tu as raison” (I admit you are right)

You can also use it before an hypothesis at the start of a sentence; to signify we consider this hypothesis as true:

• “Admettons que tu arrives à 20h chez moi, on aura jamais le temps d’y être à 20h30!” (Let’s say you arrive at my place at 20h, we won’t have time to be there at 20h30!)
• “Si on admet que le voyage dans le temps est possible, pourquoi ne pas tuer les parents de Sarah Connor ?” (Let’s say time travel is possible, why not killing Sarah Connor’s parents ?)

Hope this helped.