Here the verb uses the tu form because beau fleuve is in the second person.
One might be sceptical of that observation, because we know that inanimate objects are generally in the third person, since they can neither speak nor be spoken to. But then you have poetry. :)
The second person is associated with the vocative case, which is the form of a noun you use when you're addressing it. Latin had an explicit vocative case, meaning the noun changed form depending on whether it was being referred to (nominative) or addressed (vocative).
Although French stopped marking the vocative case visibly in noun endings, it can still give hints, such as using the particle Ô as in Ô Canada (or Alice in Wonderland's delightful "O mouse!").
However, whether or not that helpful particle is attached, we should assume that every noun is cased, even when the case is invisible. For the same reason, we assume every noun has a person, gender, and number even when these features are invisible, and are instead marked by null morphemes.
So if there is an invisible morpheme for vocative case, how do we know that our beau fleuve has it? The rest of the sentence provides a couple of clues (note that unlike a / as, these ones are audible):
The narratrice omits the article before beau fleuve.1 As a cautionary note, though, we should be careful about reading as much into the absence of articles in poetry as we would in prose.
She issues an imperative to the river. An imperative can only be issued in the second person.2
Because of these two things, we can be sure she's addressing the river, which means it's in vocative case, which means it's in second person.
Once we've established that, we can refer to this question and this one to establish that toi and not qui determines the conjugation for avoir.
1 – While the absence of an article is usually sufficient to show vocative case, it's not necessary, since one can say things like "Salut, les enfants !"
2 – Even though French grammarians also call the cohortative an "imperative" for whatever reason.
Incidentally, the idea of invisible morphemes are not without controversy. Here are a couple of other questions they raise:
You'd expect English to be heavily cased, being a Germanic language. But it only marks nominative/accusative case and only on four personal pronouns: I / me ; he / him ; she / her ; we / us. However, the existence of these pairs begs the question: does English track case invisibly on all nouns, or does it casually bring in the linguistic feature of case just for eight words? Neither theory is very appealling.
Are all French nouns in the vocative case marked for formality? Imagine I address someone: "Bonjour, Alex." If my next utterance is "Comment allez-vous ?", does the
+formal feature appear only then, or is it just agreement with an invisible
+formal feature present on Alex ? If that seems far-fetched, consider that if I use an adjective, it might well be
+feminine, and we know it's not because the adjective is inherently feminine but because it responds to the person.
Hence, not only do we have to suppose that beau fleuve is invisibly vocative... we have to suppose that it's invisibly toi, as you noted, rather than vous !