This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
Yvette Gessard-Picard was a Human woman who lived in La Barre, France during the 24th century. She was the wife of Maurice Picard, the mother of Robert and Jean-Luc Picard, mother-in-law of Marie Picard, and the paternal grandmother of René Picard. Yvette was deceased by 2364. Jean-Luc affectionately referred to her as "Maman".
Yvette used to sing "come out, come out wherever you are" to Jean-Luc when he was a young child. (Star Trek: Insurrection) She also encouraged him to "look up" at the stars and tell him wondrous extemporaneous stories, fueling his imagination and later, his interest in joining Starfleet. (PIC: "The Star Gazer", "Monsters")
As a child, Captain Picard took piano lessons; he dreaded the recitals. As he felt that he was not very good at playing the piano, he hated playing in front of large audiences. In later life, he regretted giving them up, as they pleased his mother. (TNG: "The Perfect Mate")
Yvette had a turbulent relationship with her husband Maurice, which proved a traumatic part of Jean-Luc's childhood memories. (PIC: "The Star Gazer") While Jean-Luc had long assumed this was merely due to abuse on the part of Maurice, he later realized that Yvette also suffered from severe mental illness that she refused to treat, and that Maurice handled poorly. (PIC: "Monsters") This struggle with mental illness would eventually lead Yvette to commit suicide in the 2310s, something which Jean-Luc blamed himself for. (PIC: "Hide and Seek")
Later in his own life, Jean-Luc would often imagine what Yvette would've been like had she survived to an older age. He would later tell Tallinn that he often pictured her as an old woman, inviting him to have some tea with her, and telling him that they would have a "nice, long talk." (PIC: "Hide and Seek") While in a distant section of the universe where thoughts become reality in 2364, Jean-Luc Picard experienced a brief vision of his mother where that exact scenario played out. (TNG: "Where No One Has Gone Before")
The illusory version of Yvette spoke English with a French accent in TNG: "Where No One Has Gone Before", but the real Yvette spoke with an English accent similar to that of the other Picard family members in PIC: "The Star Gazer".
A picture of Yvette was included on a page of the Picard family album that did not make it on screen.
In the comic book The Gift she was given the first name Christine.