La Barre was a village in the Bourgogne region of France on Earth. It was home to the Picard family and the site of Château Picard. (TNG: "Family"; PIC: "Remembrance", "Maps and Legends")
Jean-Luc Picard was born in La Barre on 13 July 2305 to Maurice and Yvette Picard. (TNG: "Conundrum", "Chain of Command, Part I") His brother Robert Picard lived there together with his wife and son. In 2371, Robert, with his son René, were killed when they burned to death by fire. (TNG: "Family"; Star Trek Generations)
In 2367, Jean-Luc returned home for the first time in twenty years, leading the mayor to want to organize a parade and present Picard with the keys to the city. (TNG: "Family")
In 2385, Jean-Luc Picard retired from Starfleet and returned to his ancestral home. After a contentious meeting with Picard in 2399, Admiral Kirsten Clancy referred to him as "the hermit of La Barre". (PIC: "Maps and Legends")
Several places called La Barre exist in France. Some materials created for the Picard family album implied that Chateau Picard was a Bordeaux wine and in fact certified as coming from the Bordeaux region.
Wine bottle props created for Star Trek: Picard
locate La Barre in the Bourgogne region. These props were displayed at Comic Con's exhibit Jean-Luc Picard: The First Duty in the summer of 2019. 
According to the script
for "Chain of Command, Part I", the pronunciation for La Barre was "la BAR".