Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
Soyuz TM-24
Soyuz TM-24 was the 27th expedition to Mir. Soyuz TM-24 carried a crew of three. The crew consisted of Cosmonauts Valery Korzun and Aleksandr Kaleri, and the first French woman in space, Claudie André-Deshays. They joined American astronaut Shannon Lucid and Mir 21 crewmates Yuri Onufriyenko and Yuri Usachev. André-Deshays carried out biological and medical experiments on Mir for 16 days (the "Cassiopée" mission) before returning to Earth with Onufriyenko and Usachev.