Program and programming language don't have a known translation in Arabic. برمجة and برنامج are used, even though they aren't Arabic. Is there a native word that can be used instead?
"Program" in English originally meant a structured list of things to happen (and it came from French from Latin from Greek for "edict" but that's not relevant). A computer program is a list of things for a computer to do, so the word was borrowed for that.
The common Arabic word for a structured list of things to happen is, to my knowledge, بَرْنَامَج barnāmaj. This was borrowed from Persian somewhere around 1500 years ago; while it might not appear in the Qur'an, it's been in Arabic longer than "program" has been in English. This then got verbed in Arabic just like "programming" did in English.
If you're looking for a pure Arabic form, you could potentially use something like جدول أعمال "itemized list of actions". But this would sound strange, like calling a computer program a "computer agenda" in English. I'd recommend sticking to the Persian words.