There are hundreds of written language systems with unique characters. Each writing system has a unique name for its set of characters, which is often (but not always) the name of the language itself. Not all of the writing systems have alphabets. For example:
Chinese has logographic characters representing morphemes.
Japanese has logophonetic characters representing morphemes and
sounds.
Thai has syllabic characters representing syllables.
Arabic has consonantal characters omitting vowel sounds.
Greek has alphabetic characters similar yet distinct from
English.
The English alphabet is derived from Latin characters. In general, the characters of writing systems that do not use the Latin alphabet would most accurately be referred to as:
For speakers of English, foreign characters, or foreign script, might work, since most would be inclined to say:
"It's all Greek to me!"
The Greeks have a different idiom for unintelligible:
Αυτά μου φαίνονται κινέζικα (Auto mou phainontai Kinedzika)
translated: To me this looks like Chinese.
But what goes around gets around, as some Chinese refer to English as the incomprehensible language:
雞腸 (gāchèuhng)
translated: It's like chicken intestines.
Which suggests a very informal alternative:
chicken scratch?