I think Marsheaux's best work is there original songs, but curiously, they've covered an awful lot of 80s songs, by artists as diverse as Depeche Mode, OMD, The Lightning Seeds, New Order, The Human League, When in Rome and even Billy Idol.
For today, I'm going to link to their cover of Depeche Mode's "New Life"--it's pretty representative of their style in general. Andy McClusky (of OMD fame) said that they have a "certain sort of wispy, melancholic charm." In fact, as I listen to a lot of Marsheaux, I can't help but think that that's the direction I would have loved to see Book of Love mature into--but which they didn't, sadly. But there are clear and obvious similarities.
Of course, they're not quite as clear in the cover songs, one of which I'm linking to today, but hopefully it's good enough to inspire you to seek out some of their other material.