Even before its many Star Trek: Picard appearances, Château Picard has been shipping bottles of Bordeaux across the galaxy throughout Star Trek's history. Now that he's – mostly – retired from Starfleet, Admiral Jean-Luc Picard (Patrick Stewart) keeps the family business running, a role that his father had always wanted for him. Jean-Luc Picard's issues with his father are well-documented, most notably in Star Trek: Picard season 2 when the meddling of Q (John de Lancie) allowed Jean-Luc to get to the heart of the childhood trauma at the root of their estrangement.
The Picard family line can be traced back to the 8th century, but it's unclear exactly when, or for how long the Picards have been winemakers. Maurice Picard (James Callis), Jean-Luc's father, was a traditionalist, who continued to run the vineyard without the assistance of advanced technology. This tradition was continued by Jean-Luc's brother Robert Picard (Jeremy Kemp), but it's clear from what's seen of the Château, and the vineyards, that Jean-Luc has considerably upgraded the vineyard since taking over. Here's the history of the Picard family wine, and why Jean-Luc eventually decided to fulfill his father's wishes to abandon the galaxy for the grapes of the Le Barre region.