Maurice Picard was a very traditional man who did not believe in technology. He feared the loss of values and had frequent discussions with Yvette about whether or not to get a replicator. (TNG: "Family")
Maurice opposed Jean-Luc's decision to join Starfleet, wanting him to remain home and tend to the family vineyards. The two grew estranged, and Maurice died before the two could reconcile, something which Jean-Luc regretted his entire life. (TNG: "Family", "Bloodlines")
According to a deleted scene from TNG: "Journey's End", Jean-Luc stated that he "nearly washed out my sophomore year" for several different factors, including "a teenage love affair" and "my father's death." This would suggest Maurice died about 2324.
While his sons were young boys, Maurice's father, as Jean-Luc described, deteriorated "from a powerful, intelligent figure to a frail wisp of a man, who could barely make his own way home." (TNG: "Night Terrors")
In 2369, an illusory replica of the late Maurice was briefly created by Q in order to convince Jean-Luc he was dead. (TNG: "Tapestry")
Later that year, in a conversation with Beverly Crusher, Picard compared Galen to his father, saying the former was like a father who understood Picard. (TNG: "The Chase")
In the first draft script of "The Battle", Jean-Luc Picard recalled, "My father used to say, 'Nature is the best medicine for a troubled mind.'" However, later in the same scripted scene, he considered that his father may have been incorrect, concluding, "The best medicine for a troubled mind is a good woman."
In the comic bookThe Gift, this character was given the first name "Claude" rather than "Maurice".