To me it seems the Faith of the Seven from Game of Thrones has some commonalities with the medieval Catholic Church. Do any of the FotS's rituals involve sacred wine?
No usage of sacramental wine has been depicted so far in any of the books and in neither of the two TV shows.
That being said, you are correct that the Faith of the Seven is based on the medieval Catholic church - that has been stated by George R.R. Martin himself:
George R. R. Martin based the Faith of the Seven on the medieval Catholic Church, although it borrows from other elements as well. The Faith's central doctrine that there is one god who has seven aspects—the Father, the Mother, the Maiden, the Crone, the Smith, the Warrior, and the Stranger—is based on the Catholic belief that there is one God who has three aspects: the Father, the Son, and the Holy Ghost.
Martin has also stated that the amount of power the Faith has, similarly to the Catholic Church, in great part depends on who was chosen as High Septon or Pope. The Faith Militant is loosely based on crusading orders, e.g. Knights Templar and Knights Hospitaller.
Martin talks a bit more on the seven aspects vs. the Holy Trinity relation in this video.
Taking this into account there is a possibility that wine as an element of a liturgy may appear in one of the future books, TV shows or episodes of House of the Dragon.