Is the Friday Prayer Prayer Fard or Sunnah?
According to the Hanafi school, the Friday prayer is decisively established (qati`) and personally obligatory (fard al-`ayn) for men who fulfil its conditions.
The Established Obligation
The obligation is established from the words of Allah, Most High, “O believers, when proclamation is made for prayer on the Day of Congregation, hasten to God’s remembrance and leave your trading” [62:9]. The remembrance here refers to the prayer itself. Some said that it refers to the sermon (khutba) and some said it refers to both; either way, it establishes the obligation.
It is also established from the words of the Messenger of Allah (Allah bless him and give him peace) from a longer narration, “Know that Allah, Most High, has made the Friday prayer obligatory upon you” [Ibn Majah] and “Whosoever misses three Friday prayers by taking the matter lightly, Allah will seal his heart”. [Tirmidhi]
Therefore, as the texts state, it is explicitly even more emphasised than the Noon (Dhuhr) prayer and it is what is called for on Fridays. The Muslims have concurred from the time of the Messenger of Allah (Allah bless him and give him peace) until this day of ours that the Friday prayer is obligatory.
A Note on Women attending the Friday Prayer
In our school, attending the Friday prayer is not obligatory for women; however, if she does attend, it fulfils her obligation.
Actions are only by their intentions, therefore she does not lose out on any reward by not attending the Friday prayer, rather, her reward will be greater if it is done out of following the Divine command, the sunna of the beloved Messenger of Allah (Allah bless him and give him peace) and being grateful for being able to worship Allah in the way that is most pleasing to Him.
And Allah knows best.