Paris does not know about the marriage of his beloved Juliet to Romeo. When he comes to visit her, he is paying his last respects to his fiance; however, he does not make it far into the tomb before he sees Romeo entering the tomb. Since he knows Romeo killed Tybalt, Paris thinks the Montague has come to desecrate the tomb of Juliet and Tybalt.
This is that banish'd haughty Montague
That murdered my love's cousin—with which grief(50)
It is supposed the fair creature died—
And here is come to do some villanous shame
To the dead bodies. I will apprehend him.
Stop thy unhallowed toil, vile Montague!
Can vengeance be pursu'd further than death?(55)
Condemned villain, I do apprehend thee.
Obey, and go with me; for thou must die.
Romeo, not recognizing Paris in the dark (he does not have a torch) fights and then kills Paris. It's not until after he kills Paris does he realize who it is that he has killed.
In faith, I will. Let me peruse this face.
Mercutio's kinsman, noble County Paris!