La Barre was a village in France on Earth. It was home to the Picard family
Jean-Luc Picard was born in La Barre on 13 July 2305. (TNG: "Conundrum") 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", "Chain of Command, Part I"; 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")
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.
According to the script
for "Chain of Command, Part I", the pronunciation for La Barre was "la BAR".