How did the Trojan war start n the movie troy?

In the movie, Helen and Paris begin an illicit affair while he and his brother, Hector, are visiting Sparta to reaffirm peaceful relations between Sparta and Troy. They decide that she will come back to Troy with him, forsaking her vows to Menelaus. It wasn't until they were well underway that Hector discovered the truth and, to save both Paris and Helen from execution, decides to allow them to go back to Troy, knowing war will follow.

In the movie, Agamemnon is portrayed as being a greater king than he was in the Iliad. In the movie, he uses Achilles to win battles against other city-states, forcing them to pay tribute to him and acknowledge him as high king. Agamemnon, uses his brother's anger to take war to Troy, with hopes of conquering the powerful and extremely wealthy rival city.