The short answer: No. The Pope didn't say anything like that; the Pope didn't say anything remotely near that.
This is possibly the most bizarre case of papal malreportage I've seen since I started writing. Somehow, Pope Francis' simple reassertion of orthodox teaching about the future renewal of creation got transmogrified into a declaration that animals go to heaven.
Let's begin with the papal general audience of November 26,
as reported by Zenit. The general audience has often been an opportunity for the reigning pontiff to catechize the people directly, as well as to make remarks on current events or give a report on what he's been doing the last week.
Francis began the homily, "In presenting the Church to the men of our time, Vatican Council II was
very conscious of a fundamental truth, which must never be forgotten:
the Church is not a static, still reality, an end in herself, but is
continually journeying in history towards the ultimate and wonderful end
which is the Kingdom of Heaven, of which the Church on earth is the
seed and the beginning. ... And some questions arise spontaneously in us: when will this final
passage happen? What will the new dimension be like, which the Church
will enter? What, then, will happen to humanity and to the creation that
surrounds it?"
The end towards which the Church journeys, "Paradise", is "[m]ore than a place, it is ... a 'state' of mind in which our most
profound expectations will be fulfilled overabundantly and our being, as
creatures and children of God, will reach full maturity," said the Pope. "We will
finally be clothed with joy, with peace and with the love of God in a
complete way, no longer with any limit, and we will be face to face with
Him! It is beautiful to think this,
to think of Heaven. All of us find ourselves down here, all of us. It
is beautiful; it gives strength to the soul."
So far, so good. Then:
At the same time, Sacred Scripture teaches us that the fulfilment of
this wonderful plan cannot but be of interest also to all that surrounds
us and that issued from the thought and heart of God. The Apostle Paul
affirms it explicitly, when he says that "creation itself will be set
free from its bondage to decay and obtain the glorious liberty of the
children of God" (Romans 8:21). Other texts use the image of a "new
heaven" and a "new earth" (cf. 2 Peter 3:13; Revelation 21:1), in the
sense that the whole universe will be renewed and will be freed once and
for all from every trace of evil and from death itself. What is
anticipated, as fulfilment of a transformation that in reality is
already in act since the Death and Resurrection of Christ, is,
therefore, a new creation; not, therefore, an annihilation of the cosmos
and of all that surrounds us, but a bringing of everything to its
fullness of being, of truth and of beauty. This is the plan that God,
Father, Son and Holy Spirit has always willed to realize and is
realizing. [Bold and italic fonts mine.—ASL]