This is a good question. This is where the book and movie differ greatly. In the movie, Troy, the Trojans are in Sparta to make a treaty of peace. In fact, Menelaus stands up and gives a toast of peace. Hector and Paris stand up and agree to this peace. When this scene ends, there is great festivity. Paris slips into Helen's room. He bolts the door.
Helen says, "you should not be here." Paris then answers, "that is what you said last night and the night before." The point is that Helen and Paris has been having an affair when Paris and Hector came to Sparta on a visit of peace.
Paris finally asks Helen to come to Troy and Helen does. They are madly in love. Helen confesses her love for Paris. Paris does the same. In the next scene the Trojans are going back home on their ships. Paris shows to Hector that Helen is on board.
There is no hint of the mythological story of the judgment of Paris.