Hinton's and Abbot's publications are about extra non ordinary dimensions, but Camille Flammarion's publications are not. The fourth dimension –as an extension of our tridimensional world– and life out of our planet are totally different concepts, but both ideas are representative of the way that some open-minded people think.

Cover page of
Fontenelle's Conversations
Possibly influenced by Fontenelle's book, Flammarion also wrote another book: La pluralité des mondes habité (The Plurality of Inhabited Worlds), published in 1862, that initiated him as a great science fiction writer and a leader of the Pluralism. The Plurality of Inhabited Worlds has been translated into many languages and reprinted many many times.
The titles of both books are very similar, but even when Fontenelle's book came earlier, the idea of life in other planets, specially in the Moon was not new to Flammarion not even for Fontenelle.
Fontenelle's book was one of the first literary works that defended Nicolas Copernicus' theory of geocentrism, stated about a century and a half earlier. The book was not only a groundbreaker in the aspects of extraterrestrial life and the geocentric view of the Solar system; it was written in French, not in Latin, the official language of the Church and the academics. Copernicus' revolutionary theory (1543) was written in Latin; that's why the book was titled The revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres).
Fontenelle's arguments for supporting life in the Moon are very weak. Some extracts from his book tells it all:
What accounts do yo receive? enquired she. Those, I replied, that are given us by the learned who travel there every day by assistance of telescopes. They tell us they have discovered in the moon, earth, seas, lakes, elevated mountains, and profound abysses.
... in fact our description of the moon is so particular, that if a learned mas was to take a journey there, he would be in no more danger of losing himself than I should in Paris.
Another argument he uses is the story of a man called Astolfo, a character of the epic Orlando Furioso (Furious Orlando) by the Italian poet Ludovico Ariosto. At left is shown two facing pages of Orlando Furioso. Below follows a passage of Fontenelle insertion on his book of Lodovico's Orlando story.Astolfo, a valourous knight-errant was one day carried by his hippogriffe ["A legendary creature, supposedly the offspring of a griffin and a mare"] to the terrestrial paradise, which was at the top of a very high mountain: there he met St. John, who informed him that it was necessary, in order to cure Orlando of his madness, for them to take a journey together to the moon. ... his astonishment however increased when he saw in it rivers, lakes, mountains, forests, and, what I should have been equally surprised at nymphs hunting in the forests. But the most curious thing of all he saw was a valley in which was to be found every thing that was lost on the earth...
The illustration shown here was used in one of Entretiens' edition. Note that the planets are orbiting around the Sun. The Sun, as postulated by the Copernican theory, is at the center of the Solar system. Note also that all other stars are solar systems, each one has planets or orbs orbiting around them. However, our Solar system is at the very center of the universe. Somehow, Fontenelle was unable to liberate himself from the archaic Greek and Ptolemaic theories of an Earth-centered solar system: at some place or another the universe must have a center.But there is a virtue in this book that makes it outstanding: it was written with the female readers in mind, and with the intention that it should be easily understood by everybody; not only experts in the field of astronomy. The "other worlds" to which Fontenelle refers are simply the nearby planets. Now, when people speak of "other worlds" are referring to extrasolar planets in other Solar systems.
At left is shown a 1791 print titled Fontenelle meditating about the plurality of worlds. The print depicts Fontenelle with a telescope and -possibly- his dog, meditating about life on the Moon. Note the curious the way in which the Moon was painted: the Moon is framed within a clouds frame, its like emphasizing the idea of two different worlds, its a frame within another frame. But more than this, the moon is also contemplating Fontenelle (Click on the figure to see it enlarged). The logic is straightforward: other worlds are inhabited and we are contemplating them from Earth, then from those worlds somebody must also be looking at us.But besides his wrong ideas (more justly said, extravagant ideas, but not a lunatic) of life in the Moon and other nearby planets, at his time he was right about some of the future humankind's achievements:
The art of flying is but in its infancy; in due time it will be brought to perfection, and some day or other we shall get to the moon.

July 20, 1969. NASA
At right is shown the photo of a footprint of an astronaut during their Moon landing. This and other photos are still under controversy for a supposed NASA scam, but it does not matter if the landing was true or not, what matters is that sooner or later, someday, all planets and moons of our solar system will be visited or "landed" because extraterrestrial traveling has been a dream of all mankind for all its history.