1.2: Paris asks Lord Capulet if he can marry the thirteen-year-old Juliet.
1.5: Though he has no lines, Paris dances with Juliet at the Capulet's party. Somehow, though, Romeo gets to kiss Juliet and he doesn't. (Paris doesn't realize this, of course.)
3.4: Even though the Capulets are mourning for Tybalt's death, Paris shows up hoping for news that Juliet wants to marry him. Lord Capulet is worried that his daughter's grief over her cousin's death is out of control, so he asks Paris if he would be willing to marry Juliet right away, that very week. Paris agrees.
4.1: Paris goes to Friar Laurence to arrange the details of the wedding. Friar Laurence is not too thrilled about the idea of Paris marrying Juliet. Then Juliet shows up, and Paris greets her enthusiastically. She seems to still be very upset over her cousin's death, and she answers his questions strangely. Friar Laurence suggests Paris should leave so Juliet can have confession. So Paris gives her a chaste kiss and tells her he'll see her at the altar.
4.5: Paris arrives at the Capulet's house fresh-faced and excited. It's the morning of his wedding, and finally, he gets to marry Juliet, the girl of his dreams. Instead, he finds everyone grieving at her bedside. Juliet is dead.
5.2: Paris, shocked that Juliet had the nerve to die the night before they are supposed to be married, grieves quietly by Juliet's tomb. Outlaw Romeo shows up, and Paris assumes he's there to cause trouble for the Capulets. He and Romeo fight, and Romeo kills him. Afterwards Romeo feels bad, since Paris was basically a nice guy.