I can't find evidence in any English dictionary that this word exists (all uses of it that I can find in the 18th century are in French sources and are proper nouns, mostly surnames or place-names), and no evidence that I can find that this poem existed any earlier than 1996, when George Grant published it in The Patriot's Handbook. Although he called the poem a "widely circulated verse," there is no evidence that I can find of it before this date. This strongly suggests that Grant fabricated the poem, or perhaps republished it unquestioningly from an unreliable secondary source.
If that is the case, the question is "what did the author mean for us to think aubaud means," and we can only guess from context. This is not easy, as the convoluted syntax throughout the poem doesn't yield clear meaning easily. It reads as if a modern author relied on the fact that modern readers find 18th-century texts difficult to parse in order to cut corners. The third line is difficult to interpret because the second is also hard: "magistratal," in every use I can find, is an adjective, and it's difficult to parse the number, tense, and object of "laud." The third line makes adequate sense without the word "aubaud" anyway; temporal power is given by God "to advance creaturely happiness." We're left to intuitively grasp at similar-sounding words; "abroad" seems like a reasonable choice (and I wonder why the author didn't simply use it).