Yes, "sur le bord de l'eau" translates to "by the waterside" (word for word "on the side/bank of the water").
Bordeaux was founded 3 centuries B.C. and was then called "Burdigala" in Gaulish. It might comes from "burd" (cove) and "gala" (marsh). It might... but we don't know for sure, some people have other theories. Anyway, whatever the original meaning, the name Bordeaux evolved from it.