Here is the breakdown of Ecclesiastes Chapter 3:
I. Look up: God orders time (Ecc 3: 1-8)
II. Look In: Eternity is within you heart (Ecc 3: 9-14)
III. Look Ahead: Death is Coming to All (Ecc 3: 15-22)
Ecclesiastes is not making a pronouncement on the eternality of animals. That isn't the theme of the book, nor is it the theme of chapter 3. Ecclesiastes is a book of wisdom. It is not a book establishing doctrine of soteriology (that's why there is the book of Romans); or any other church or New Covenant doctrine for that matter. If you read chapter 3 (or the whole book for that matter), you would find the wisdom Solomon is pointing out: There is a pattern that is inescapable: we all die. That is the main idea in chapt 3, and we share that in common with the animals. Psalm 49 also repeats this idea.
Melancholy as the tone of Ecclesiastes is, "The Preacher" concludes that all is vanity on earth, and that the end of the matter is for man to fear God, and keep His commandments (last two verses of the book).
The fact of the matter is, Scripture is silent on this issue, and Francis spoke outside of Scripture.
If we fixate on an cute, cuddly animal (and push out of our minds the babies eaten by dogs and such) and their eternal state, doesn't that become an idol, diminishing the special creation man is, and the rescue mission Jesus was sent to perform?
The Gospel and the cross of Jesus Christ becomes all that much bigger when you consider God has his eyes squarely on humans. Animals server their purpose. But the New Covenant has no provision for them.