What is the ruling on reciting Surat Al-Jumu'ah and another surah in the Fajr prayer on Friday?

There is nothing to prevent the recitation of Surat al-Jumu'ah or other surahs at Fajr prayer on Friday, due to the generality of Allah’s Almighty saying: (So recite what is easy [for you] of the Qur’an).

However, it is better to recite Surat as-Sajdah and Surat al-Insan, following the example of the Prophet, peace and blessings be upon him. For this reason, Shaykh al-Islam Ibn Taymiyyah said: "The secret behind reciting them in the Fajr prayer on Friday is that they encompass what has been and what will be on that day. They include the creation of Adam and the mention of the معاد (Resurrection) and the gathering of servants, which will take place on Friday. So, in their recitation, there is a reminder for the servants of what has occurred and what will occur on that day."

It is permissible to recite Surat al-Jumu'ah at Fajr on Friday, as long as one does not consistently do so believing it to be a Sunnah. For, consistently performing what is not legislated, believing it to be legislated, is an innovation (bid'ah).