Sorry ladies. Here's how the French say it:

BOO-EE-GUE

BOO as in BOOt

EE as in E-mail

GUE as in roGUE (very quickly)

There is no "Boy" sound and the final S is mute (as always in French).

Bouygues is a big French corporation that started in the construction business but is mostly known, to my knownedge, as a cell phone operator also involved in the media (TV and/or cable, not sure).

I looked on Youtube for one of their ads but most of them don't say the company name. In this one, it's said at the very end: http://youtube.com/watch?v=huV-gE8rcAw (and there's nice kitties in the ad so it's worth watching)