English, unescapably, as I think in it. There is a rather large vocabulary, with a somewhat substantive (though not to the same degree as English's) number of foreign borrowings, some of them fairly recent judging from their morphological shape, and most of them relating to food. Also, some varieties distinguish /eː ɛː/ as separate phonemes (however not /oː ɔː/).
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Danish, Swedish, and Norwegian — most nominals inflect for definiteness; the language itself is also a part of a dialect group that are still, in some cases, of about the same degree of mutual intelligibility (but it's often asymmetric), though with distance, one does, of course, tend to find greater degrees of divergence. The degree of written intelligibility between this language and its near relations is very, very high. This is at least in part owing to a situation similar to that which created Norwegian Bokmal — the language in question enjoys very widespread use in literature and other culturally significant productions, and a great deal of scientific literature in-setting is written in it. Most speakers of regional "dialects" have greater understanding of the "standard" than the other way round.
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Several other Indo-European languages, including Proto-Indo-European (I'm fond of paradigms that are not wholly neat and regular), Classical Latin, Ancient Greek, French, and Spanish; I'm fond of how morphologically complex they all are — and have ended up developing some rather complicated nominal declensions (three numbers — singular, collective, and plural; each in both the definite and indefinite, with some forms being contracted and consequently rather irregular-looking). Front rounded vowels also occur at times (but only allophonically), and a distinct /l/ phoneme has been attained.
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Various not-developed (or not well developed) languages appearing (or implied to exist) in fantasy worlds I've enjoyed.
(1) From George MacDonald (a perennial favourite with me), we have snatches with names such as Anodos, Lona, Odu. While none presently exists, all three are phonologically valid, as are Photogen (though not Watho or Nycteris), .
(2a) Japanese ideas of what a fantasy language would sound like, taken from some rather obscure sources: background music appearing in a few video games, notably Tales of Legendia (a bit of a messy title, but the overall aesthetic of the game has been massively influential on my worldbuilding), which are difficult to make out, but sound like Mel fa riaridak raera/Kidakufa erearae/Rashite ara (ite ara) ite noste ara, ni ihara na wa amen des ba shi ite emara, Mei ha inochi ba idore na ito e sereba, bei fa inochi no ha re/Menina daski ibana nyal vina idagida — fairly close to Japanese, but with some aberrations, like final -s, -l, ambiguously a /v/ phoneme. Similar to this, a line of distorted chanting appearing in Xenogears sounds awfully like tudolsensepuerolkaskan.
(2b) Tales of the Abyss also contributes the line tue re ze croa ryou tue ze, &c., which does point to the very limited consonant clustering (usually only voiceless stop + /l r j/) that appears in a few cases, mostly longer compounds and proper names.
(2c) The vaguely Europea sounding names Ginevia and Ahanas appearing in the Windaria film. From Studio Ghibli, the also vaguely European Pazu, Sheeta, Dola, Muska appearing in Castle in the Sky, and somewhat Finnish-sounding, Osono, Tonbo (yes, this is just the Japanese word for "dragonfly", I know), Kopoli/Kopori (the word kopori actually means "glass" or "vitrification" in the language, too; cognate to Japanese 氷 "kōri" - "ice"), and the name of the city, Coriko, Koriko or however one wishes to spell it.
(3) I listened to Enya a great deal growing up, so there's likely some subconscious thoughts of Irish in there somewhere. Not quite a fantasy language, but it sounded like one to me at about age ten or so.
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And, of course, Japanese, but more specifically its former literary register Bungo; the verbal system has many structural parallels, the orthography is quite similar (I remain torn on which, if any, Kana ought to be directly borrowed from Japanese, but I do think such a system would emerge; the stages I've shown thus far all use a Man'yōgana like system, but characters do remark that old texts are rather difficult to read (one also describes Ancient Ifsumé as sounding as if it were all chopped apart; because of both changes in sounds and morphology, he is only able to understand those words that have undergone relatively little change.
Adjectives are also quite verbal in how the function, having a wider range of conjugations than the ones in Japanese currently do. They can, and frequently do, predicate sentences. The classical copula あり ("ari") also influenced the development not only of the copula in this language, but an entire class of similar -ri verbs, which tend to mean "become something" or "make something like or into something else". The principal parts of the six-stem verbs remain fairly similar in usage (though there is a much greater emphasis on tense, with a conjugated quasi-future), monosyllabic verbs are not at all rare, and the equivalent to the Kana orthography has not been much adjusted to match historical sound changes since it was introduced.
There are, of course, the noteworthy departures I've mentioned desiring: native words are used far more often than borrowed ones, even for technical and scientific vocabulary (though a number of words for items of foreign cuisine and nativised plants have been imported, as have those for certain objects associated with ways of doing things for which there were no very good native equivalents). Most of these come from what is called the Kokori language, one that plays an important role in some stories I've written, but which is now nobody's mother tongue, having been rediscovered after a long period of disuse (its decypherment leading to quite the internal revolution in gastronomy). From the forms of the words borrowed, it would appear to be some form of Langue d'Oĩl.
Also, of some note, the culture was initially wheat-growing, with wet rice agriculture being a later introduction; consequently, while some parts of society have a more collectivist mindset, others tend to be more independent. The speakers are also in a place more geologically stable than Japan. The result is a culture quite markedly different — there aren't any honorifics, and equivalents to keigo are also virtually non-existent, though there are plenty of ways to apologies, express thanks, &c., as in most languages — and I often find myself amused by such differences (of course, creating the language is meant to be fun, so it has achieved at least one goal.