If I entered the prayers on Friday and the Imam had already started the prayer. Do I pray two Rak'ah or do I have to pray four Rak'ah?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Missing the Khutbah does not have any impact on the validity of the Friday prayer itself, although the Khutbah is very important and attending it makes the person entitled to a great reward.

So, if you come while the Imam is still in the first Rak'ah, you join in the prayer and complete with the Imam the two Rak'ahs and pronounce the Salaam just after the Imam.

If you miss the first Rak'ah with the Imam, you pray the second Rak'ah with the Imam, and when he pronounces the Salaam, stand and make up for the Rak'ah you missed.

However, if you missed both Rak'ahs, then you pray four Rak'ahs as per the regular Thuhr prayer.

Allah knows best.