The news, courtesy of People and the Daily Mail, comes as Thurman gets set to hit the small screen in the five episodes of the NBC series "Smash," starring Katharine McPhee and Debra Messing.
The "Bel Ami" and "Kill Bill" actress, 41, has two children with actor ex-husband Ethan Hawke: 13-year-old Maya and 10-year-old Levon.
Thurman and Busson, 49, have been together since 2007, with a short split in 2009.
As for "Smash," look for Uma playing "a famous and somewhat difficult movie star," according to EW.
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