The site I found, a (commercial) history of the Knights Templar, offers tsuwm's "Be glorious (noble)!" as one possible meaning of the banner's name, but they're not sure, either:

The word beau is now generally conceived to mean beautiful, but it means much more than that. In medieval French it meant a lofty state, for which translators have offered such terms as "noble,""glorious," and even "magnificent." As a battle cry then, "Beau Seant" was a charge to "Be noble" or "Be Glorious."

...Other etymological suggestions include piebald, which is perhaps closer to the mark. Piebald means spotted or two color as in a piebald horse or cat. This certainly fits the description of the Beauséant, for it consisted of a black square above a white one.


http://templarhistory.com/beauseant.html