What doctrinal value does the Catholic Church place on "Cantate Domino"? If I understand correctly, Cantate Domino is a papal bull by Pope Eugene IV which is in some way affiliated with the Council of Florence.

I have heard it claimed that the writing of Cantate Domino was an instance of papal infallibility, but if I understand correctly, there are very few instances in which it is widely agreed that a pope spoke ex cathedra, and Cantate Domino is not one of them.

That being said, the Council of Florence is an ecumenical council. My understanding is that some but not all aspects of ecumenical councils are infallible. Was the writing of Cantate Domino an instance of the infallibility of ecumenical councils? What is the precise relationship between Cantate Domino and the Council of Florence?

If not, is Cantate Domino nevertheless a product of the (infallible) Sacred Magisterium? Or is it merely a product of the (fallible but authoritative) Ordinary Magisterium?
Documents of ecumenical councils receive their authority from the Pope who solemnly approves them. Councils give council to a Pope, and it is by his authority alone that their documents can be infallible.

Conciliarism, which teaches that a general council of the Church has higher authority than the Pope, is a condemned heresy. The First Vatican Council's infallible document Dei Filius, ratified by Pope Pius IX, stated:


  …they err from the right course who assert that it is lawful to appeal from the judgments of the Roman Pontiffs to an œcumenical Council, as to an authority higher than that of the Roman Pontiff. 



We can judge whether a document is infallible based upon whether the Pope


speaks for the whole Church,
invokes all his authority,
intends to definitively define dogma, and
speaks regarding the faith and/or morals.


These conditions follow from the section of Dei Filius regarding papal infallibility:


  …we teach and define that it is a dogma divinely revealed: that the
  Roman Pontiff, when he speaks ex cathedra, that is, when in
  discharge of the office of pastor and doctor of all Christians, by
  virtue of his supreme Apostolic authority, he defines a doctrine
  regarding faith or morals to be held by the universal Church, by the
  divine assistance promised to him in blessed Peter, is possessed of
  that infallibility with which the divine Redeemer willed that his
  Church should be endowed for defining doctrine regarding faith or
  morals; and that therefore such definitions of the Roman Pontiff are
  irreformable of themselves, and not from the consent of the Church.


The four conditions are indeed satisfied in Cantate Domino (1442) since Pope Eugune IV


speaks for the whole Church: "The most Holy Roman Church firmly believes, professes and preaches…"
invokes all his authority: The document is an authoritative papal bull.
intends to definitively define dogma: In this case, he is not defining anything new; he's only relaying and reaffirming what has been said before him (like in Pope Boniface VIII's Unam Sanctam of 1302) regarding the necessity of the Church for salvation.
speaks regarding the faith and/or morals: Yes. In this case, he speaks of both.


Cantate Domino is thus part of the Extraordinary Magisterium, which Fr. Hardon, SJ, defines as:


  The Church's teaching office exercised in a solemn way, as in formal declarations of the Pope or of ecumenical councils of bishops approved by the Pope. When the extraordinary magisterium takes the form of papal definitions or conciliar decisions binding on the consciences of all the faithful in matters of faith and morals, it is infallible. 


(cf. my answer here)

The famous 20th century Catholic theologian Msgr. Joseph Clifford Fenton, in his 1958 work The Catholic Church and Salvation: In the Light of Recent Pronouncements by the Holy See pp. 31-41, considered Cantate Domino an "official pronouncement of the Church" that "simply makes more explicit the lessons brought out in the Fourth Lateran Council and in the Bull Unam sanctam."