Thurman started dating the French financier in 2007. The pair briefly split in 2009 before reuniting in 2011.
Thurman, 43, gave birth to their daughter, Rosalind Arusha Arkadina Altalune Florence Thurman-Bosson, in 2012. Thurman has two other children, daughter Maya, 16, and son Levon, 12, with ex-husband Ethan Hawke. Busson, 51, has two sons, 16-year-old Arpad and 11-year-old Aurelius, with Elle Macpherson.
Thurman memorably recurred on Smash in 2012 and most recently appeared in Lars von Trier's Nymphomaniac.