Originals: Bonnie and Clyde by Serge Gainsbourg and Brigitte Bardot (covered by Luna)
Luna recorded two versions of it with Lætitia Sadier of Stereolab in 1995, both turned up on a single and one was included as a hidden track on the end of Penthouse. The single was awareded Single of the Week in Melody Maker.
Luna with Lætitia Sadier - Clyde Barrow version (fast)
Luna with Lætitia Sadier - Bonnie Parker version (slow)
Luna (with Britta on vocals, live in Brazil 2001)
There are a stack more Bonnie and Clyde's in this post from a couple of years ago including a performance with Keren Ann and a live version from their last London show with Sonic Boom of Spacemen 3/Spectrum.