I can answer this question in a limited fashion.

I did some research surrounding Christiaan Huygens, the dutch mathematician/inventor/astronomer/natural philosopher who lived in the second half of the 17th century. Huygens' last work was a book called Cosmotheoros, published right at the end of the century (so either just before, or within the Enlightenment, depending on what you consider the Enlightenment to be). Cosmotheoros was a kind of popular science book covering the cosmos (roughly including what we would refer to as the Solar System). Half of the book is devoted to conjectures about "multiple words"--Huygen's serious and scientifically-intended speculations about life on other planets. The other half gives a kind of "mind's eye" tour of the solar system, describing various features, sizes and movements. The title is a clue to its intention: it's Greek and means "world viewer/spectator".

Cosmotheoros was published in 1698, three years after Huygens' death. He initially wrote it in French, then translated it into Latin before it was published (perhaps in order to limit his audience). However, it was immensely popular and immediately translated into English under the title "The Celestial Worlds Discover'd". Throughout the first couple of decades of the 18th century, it appeared in twelve editions and multiple language, including Dutch (1699), French (1702), German (1703) and Russian (1717) [Van Heertum, Cis. Peter the Great and Christian Huygens. The Ritman Library (http://www.ritmanlibrary.com/2013/06/peter-the-great-and-christiaan-huygens/)]

It was as popular in public intellectual circles at the beginning of the 18th century as Sagan’s Cosmos was at the end of the 20th.

Two examples of its popularity: The English astronomer John Flamsteed regularly recommended it to interested amateur astronomers (one of whom went on to establish the Plumian Professor of Astronomy professorship at Cambridge, the implication being that Cosmotheoros was an exciting, even inspiring, read. [Correspondence of Sir Isaac Newton and Professor Cotes. (London: John W. Parker, 1850). Pg LXXV (n. 158)]. Peter the Great was also a fan. He encountered it on his tour of Europe as a young man and when returning to Russia and establishing his Best of European Science setup, he was responsible for having Cosmotheoros be translated into Russian, making it apparently the first 'scientific' text to be published in the country. [Collis, Robert. The Petrine Instauration. Religion, Esotericism and Science at the Court of Peter the Great, 1689-1725. (Leiden: Brill, 2012) pgs 116-118.] It was huge. People were incredibly excited by the ideas Huygens was writing about.

This not a shy text in apparently disputing Biblical teachings, and nor is it a shy text in Saganesque discussion of the cosmos*. Here's some of Huygens' notes for the text (translated from French by me):

It is not for us to give limits to nature, and we should know... that whatever grandeur and extension we give limits to, all that grandeur is nothing compared to the space beyond it, and [these limits are] a tiny proportion [of the whole] like a grain of sand is to the whole of the Earth.

Eat your heart out, Sagan’s “mote of dust suspended in a sunbeam”! Talk about existential awareness… Cosmotheoros is thick with it. This is not the singular, small world of the Bible, but neither is it areligious. Like everything in the 17th century, God is very present:

What if these stars or suns, each also have their planets around them, and each of these planets as much as variety of creatures here on earth, what magnificence incomprehensible follows from this great work, and power and eternal wisdom which is in the master and the architect.

Huygens himself addresses the big question that you are asking—clearly this isn’t straight from the Bible. Is this sacrilegious? Here’s his answer in Cosmotheoros’ English edition from 1698, square brackets is me translating:

These Conjectures do not contradict the holy holy... The other sort [people who accuse Huygens of being sacrilegious], when they hear us talk of new Lands, and Animals enbued with as much Reason as themselves, will be ready to fly out into religious Exclamations, that we set up our Conjectures against the Word of God, and broach Opinions directly opposite to Holy Writ. For we do not there read [in the Bible] one word of the Production of such Creatures, no not so much as of their Existence; nay ra|her we read the quite contrary. For, That only mentions this Earth with its Animals and Plants, and Man the Lord of them; but as for Worlds in the Sky, 'tis wholly silent…

Huygens goes on:

…It's evident God had no design to make a particular Enumeration in the Holy Scriptures, of all the Works of his Creation… [i.e. that just because other worlds are not mentioned in the Bible, doesn’t mean that they don’t exist]

and

Since then the greatest part of God's Creation, that innumerable multitude of Stars, is plac'd out of the reach of any man's Eye; and many of them, it's likely, of the best Glasses, so that they don't seem to belong to us; is it such an unreasonable Opinion, that there are some reasonable Creatures who see and admire those glorious Bodies at a nearer distance? [i.e. That given some stars are so far away, surely it makes sense that there would be creatures created by god who can see them closer up in order to admire them?]

It’s a fabulously imaginative argument, reliant upon Huygens’ understanding of the enormity of space. Huygens isn’t concerned that the Bible doesn’t mention other worlds. The Bible isn’t necessarily all knowledge about the cosmos, he says. His final argument towards this is that if people had bowed to religious pressure earlier, perhaps some of the advances described in the book—such as the discovery of moons around Jupiter and Saturn—wouldn’t have occurred. Men have minds to search and learn and so they can.

So to answer your question: For this little corner of the Enlightenment at least, the popularity of Cosmotheoros suggests many intellectuals/elite bought into Huygens’ worldview wholly and with passion, and were more excited by the prospect of a huge universef what we would call aliens and alien worlds than afraid by it—although some, clearly were religiously opposed.

I’ll leave you with some more Saganesque Huygens:

For here we may mount from this dull Earth, and viewing it from on high, consider whether Nature has laid out all her cost and finery upon this small speck of Dirt. So, like Travellers into other distant Countrys, we shall be better able to judg of what's done at home, know how to make a true estimate of, and set its own value upon every thing. We shall be less apt to admire what this World calls great, shall nobly despise those Trifles the generality of Men set their Affections.

(Ps. I think it’s no coincidence Cosmotheoros feels so very much like Sagan’s Cosmos, right down to the way they talk about the size of the universe and the smallness of the Earth. I strongly suspect that Sagan's Cosmos is deliberately echoing Cosmotheoros --I have no real proof except their similarity as emotional, evocative tours of the solar system. However, Sagan was clearly highly familiar with Huygens' work, and Cosmos the tv show places Voyager (with which Sagan was so heavily involved) in the context of Dutch exploration--using the Huygenses as an example.)