The group is Blue Rondo A La Turk, an '80's jazz-pop band from England. Other spin-offs include Matt Bianco (w/singer Basia). Also, a group called Animal Nightlife – same genre.
Found this item on YouTube, and this other video by Working Week featuring Tracey Thorn of Everything But the Girl. Now if I could just find the version of The Paris Match sung by her, that would be great also.