How to Catch up with Friday Prayer
Question

If a person comes to the mosque on Friday and finds that the (Jumu`ah) prayer has already ended, but he finds one man who still has one rak`ah to pray, and he prays with him, should he complete his prayer as Jumu`ah [two rak`ahs] or Zhuhr [four rak`ahs]?
Praise be to Allah.Shaykh ‘Abd Al-‘Aziz Ibn ‘Abd-Allah Ibn Baz (may Allah Have Mercy on Him) said:
“He has to complete it as Zhuhr because the Jumu`ah prayer is over. You can catch Friday prayer up with one rak`ah if you catch up with the second rak`ah prayed with the imam, then you can pray it as Jumu`ah. But if you do not come until after the salam or after the second rak`ah, during the Tashahhud or when the imam is prostrating in the second rak`ah, then you should not pray it as Jumu`ah, but rather as Zhuhr. 
The Prophet (peace and blessings of Allah be upon him) said: “Whoever catches up with one rak`ah of Jumu`ah, let him add one more to it and his prayer will be complete.” (Narrated by al-Tirmidhi, 482; al-Nasai, 554; Ibn Majah, 1113)
The meaning of this hadith is that if he only catches up with less than a rak`ah then he has not caught up with Jumu`ah so he has to pray it as Zhuhr. This is what is prescribed in Islam. 
If he catches up with a person who is making up the rak`ah that he missed, and prays with him, then he should pray it as Zhuhr and not as Jumu`ah.
It should also be noted that this should be after the sun has passed its zenith. But if Jumu`ah prayer was offered before the sun reached its zenith, he should not pray Zhuhr until after the sun has passed its zenith, because it is permissible to pray Jumu`ah before the sun reaches its zenith , in the “sixth hour”, according to the correct scholarly view. But it is preferable and more on the safe side to pray it after the sun has passed its zenith, as is the view of the majority of scholars. But in the case of Zhuhr, it is not permissible to pray it until after the sun has passed its zenith , according to the consensus of the Muslims. And Allah is the Source of Strength.” (Majmu’ Fatawa Wa Maqalat Mutanawwi’ah Li Samahat Al-Shaykh Al-‘Allamah ‘Abd Al-‘Aziz Ibn ‘Abd-Allah Ibn Baz (may Allah have mercy on him), part 12, p. 329)
For more, please see these answers: 22155 , 45494 , 96836 , and 75156 . 
And Allah knows best.