Is it permissible to perform Jumu'ah prayer before the noon adhan, knowing that the mosque holds two Jumu'ah prayers: the first before the noon adhan and the second after it?

The Friday Adhan was originally a single call to prayer in front of the Khatib (preacher). Then, Uthman, may Allah be pleased with him, introduced the first Adhan to alert the people.

Scholars differed regarding the time for Friday prayer. The majority view is that it is at the time of Dhuhr (noon prayer), while Imam Ahmad permitted performing it before Zawwal (the sun's declination from its zenith). The majority relied on the Hadith of Anas that the Prophet, peace and blessings be upon him, used to pray Friday when the sun declined. Imam Ahmad, on the other hand, relied on Hadiths, including the Hadith of Jabir, which indicated that they prayed Friday and then dispersed when the sun declined.

In conclusion: It is preferable to act according to the majority view, which is to perform the Friday prayer after the entry of the Dhuhr time. As for repeating the Friday prayer in a single mosque, it is an innovation (bid'ah).