Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Muslim scholars have two different opinions concerning the time of Friday prayer. (A) The majority of Muslim scholars are of the opinion that the time of Friday prayer is the same as the al-Zuhr prayer. So, it is not permissible to call Azan whether it is the first or second before its fixed time. The Azan or the sermon for Friday prayer is not valid if they are made before that time.
(B) Imam Ahmad is of the opinion that the time of Friday prayer starts before the sun passed the meridian. According to him, the time of Friday prayer is after the sunrise when the sun has completely risen to the length of a spear or two spears about the horizon, i.e. twenty minutes after sunrise, since it is a feast prayer so it is similar to the prayers of two feasts. He cited as proof the Hadith of Abdullah Ibn Sedan al-Sulami -in al-Musnad - who said: 'I prayed al-Jumu'ah with Abu Bakr , and his sermon and prayer were before noon. Then I prayed al- Jumu'ah with 'Umar and his sermon and prayer were at noon as I assumed. Then I prayer with 'Uthman and his sermon and prayer lasted until after the sun has passed the meridian, and no one scolded either for it' .
It is narrated in Musannaf Ibn Abi Shaibah from Abdullah bin Salamah who said: " Abdullah bin Masoud led us in Jumu'ah prayer and he performed it at forenoon and then said: 'I did so, because I was afraid of the heat for you" . The same practice is reported from Mu'awiyah , Jabir , Saeed bin Zaid and Sa'ad bin Abi Waqqas (Radiya Allahu Anhum).
Therefore, if the responsible persons at the mosque support the later opinion and they rely on the Fatawa of some scholars who support this thought of school, in such a case the practice is correct and you may perform prayers with them. Know that -Al-hamdulillah- there is flexibility in this matter, especially if there is no other mosque. If you perform Jumu'ah with them, your prayer is correct, so you should not repeat it.
However, if they do so based on their own wishes without relying on the Fatawa of Muslim scholars then it is not permissible, and you should exhort them and explain to them this ruling. No doubt performing al-Jumu'ah prayer when the sun had passed its meridian is better since it is the opinion of majority of Muslim scholars; even Hanabilah are of the opinion that performing the prayer at the time of Zuhr is better.
Allah knows best.