I am a teacher of English as a Foreign Language. That means that I teach the English language to people who are learning in a place where English is not the primary language of everyday interaction.
Remember that where I live, in Japan, the word foreign is translated as alien when it comes to people. The words foreign language in English are most frequently translated as "gaikokugo" "外国語” or outside country language as a direct translation of the Chinese characters. Remember also that gaikokujin is translated as alien.
This may seem like I am stretching an idea to it's breaking point, but here is my conclusion up front. My students are traumatized in school by English. It is sold to them as a thing so far from their own natures as to be feared or reviled.
The alien language concept is a disservice to humankind. It is a construct of masculine, reductionist science, with it's agenda of distinguishing discrete forms as one method of control.
English, and all other languages are only foreign because they evolved in slightly different ways as humanity spread out across the globe from it's origins somewhere around 100,000 years ago according to Noam Chomsky's theories.
New words are formed or borrowed by all living languages, and languages become extinct as the last native speakers of the language die off.
Written languages came after spoken languages, because writing is one step further along the route of abstraction. People decided that if they could somehow record stories in a more perminant form, it would be helpful, so the someone came up with the idea of a set of symbols that would represent the sound of spoken words, or ideas in the case of pictographic syllabaries.
Language is a Psychokinetic, Telepathic Act
Language is evidence that psychokinesis and telepathy exist and that most humans posses the ability. First the mind conceives of an idea that the thinker wants to transmit. The thinker then uses psychokinesis to move muscles in the body in order to control breath and muscles in order to make sounds that the listener, the receiver, can collect in order to translate them into meaning in their minds.
It not only transmits meaning, but emotion and feeling that causes those who understand to manifest physical reactions, the production of saliva when told about food, tears when told about loss, increased blood flow when told about sexuality, and physical flight when told about danger.
This was also found to work with symbols, so instead of creating sound, marks were made on a physical object that would carry and transmit ideas into the mind of the beholder, soliciting the same range of feelings and physical reactions as speech.
Another way humans communicate with each other is through body language, the ultimate manifestation of this being signing, usually used by people who would find it difficult to translate sounds into meaning. And with this kind of communication, there is often less information transmitted intentionally than with verbal or written communication forms. The movement of the extremities, the angle and distance of the speaker to the listener, and facial expressions often communicate truth more clearly than words or symbols.
So What Would a Truly Alien Language Look Like?
There is a branch of linguistics called xenolinguistics, exolinguistics, or astrolinguistics where scholars knock this question about. Since these branches of linguistics are hypothetical, there is no way to tell for sure, but let's think about methods for communication that exist on earth that we have yet to understand.
Cetaceans use clicks, whistles, pops, groans and moans to communicate with each other possibly as far away as the other side of the planet. Insects use pheromones to communicate ideas like, "I am a baby, feed me," or direction. The bodies of squids change texture and exhibit moving colors to communicate with their own and other species. Up to 90% of ocean creatures are bioluminescent, and probably use that ability to communicate a variety of messages.
Humans on earth developed syllabaries up to 8 thousand years ago that remain undeciphered even now, like Jiahu symbols or or Banpo symbols.
There are indeed truly alien languages around us, unrecognized, and uninterpreted. There is no reason for governments to manipulate human languages to make them artificially difficult.
Induction into the power and mystery of language is what we should aim for, not the creation of artificial difficulties.