Dear Zafreen,
As-salamu alaykum
The Arabic script of the Quran has arguably been adopted and adapted for use in other languages which are not necessarily from the Semitic stock of languages such as Persian and Urdu, arguably due to the spread and penetration of Islam. However, I am not clear what you mean by an 'Indo-European' script. The earliest Arabic scripts of the Quran are arguably from the Hijaz region of the Arabian Peninsula (known as the 'Hijazi' script). The Kufic and Masq script are other early known Quranic scripts.
The source of the Arabic alphabets itself is by some considered to find its roots in the Nabatean language who allegedly wrote in a derivative of the Aramaic alphabet.
Regards,
Joseph