Jean-Luc Picard is the captain of the Enterprise-D in Star Trek: The Next Generation and captain of the Enterprise-E in the films Star Trek: First Contact, Star Trek: Insurrection and Star Trek: Nemesis.
Picard is of French ancestry, and his family still maintains a vineyard in France. He never married, in spite of his "paradise" being revealed as a family Christmas in Star Trek: Generations (of course, he got tired of that in five minutes, so whatever). There are occasional hints of a love interest between him and Dr. Beverly Crusher, but it is never fully pursued in the series. At some point after the TNG series, they do marry and later divorce in a Q-induced alternate reality in the series finale. Picard also seems to take on the role of a father figure to Dr. Crusher's son Wesley.
Picard first gained fame in the Federation at the Battle of Maxia, where he was serving on the USS Stargazer. A Ferengi ship launched a surprise attack on the Stargazer, causing heavy damage. Through a quick warp maneuver which would come to be known as the Picard Maneuver, he caused his ship to appear in two places at once. The Ferengi ship fired on the wrong image, allowing the Stargazer the opportunity to destroy its opponent.
Picard was assimilated by the Borg in the TNG episode "The Best of Both Worlds", taking on the identity of a Borg "spokesperson" named Locutus. He was subsequently rescued by the crew of his starship, but the incident left lasting mental scars and a deep hatred of the Collective.
The entity known as the "Q" took personal interest in shaping Picard's course in life. Q tested Picard on multiple occasions, trying to expand Picard's thinking (supposedly; many think Q was just doing it for shits and giggles), most notably in the TNG pilot and finale. In another example, Picard suffered a life-threatening injury while at Starfleet Academy, requiring the implantation of an artificial heart. A subsequent electric shock damaged that heart, and Picard believed himself dead and wished he had never gotten into the altercation that resulted in his injury. Q showed him what his life would have been like had he chosen that path, and Picard quickly realized his life was far better with the original course of events.