All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
To perform the Qunoot supplication specifically during the Friday prayer is a religious innovation, as it was not reported that the Prophet or his companions specifically performed the Qunoot supplication during the Friday prayer.
Some scholars, among the Taabi'is (the generation which followed that of the companions) and the generation which followed them, stated that the Qunoot supplication during the Friday prayer is a religious innovation unless the Imaam was supplicating in his prayers due to a calamity which befell the Muslims and Friday prayer was among those prayers; as indicated by Imaam Ash-Shaafi'i .
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Allaah Knows best.