There are no official words that the penitent says in any language, though there are traditional words that vary geographically, and general requirements (the penitent has to convey contrition and purpose of amendment, mention type and number of mortal sins, etc).
AFAIK, the closest thing to a “formula” for the penitent is the formerly prescribed Confiteor which was supposed to be said before listing one’s sins. The old Roman Ritual (Part V, Chap. I, Para. 16) states:
The penitent says the “Confiteor,” either in Latin or in the vernacular, or at least the following words: “I confess to almighty God and to you, father.” Next he confesses his sins in detail, being aided whenever necessary by the priest. …]
I don’t know how widely this was observed before Vatican II, and I don’t think it is observed much if at all today. And there’s a good chance that if you start reciting the Confiteor in Latin, the priest will have no idea what you’re doing. Even if he knows Latin, most priests just want you to get to the point, especially if there’s a line.