We get to try somebody in an American court for a crime committed in Libya?

Trial opens of Ahmed Abu Khattala, alleged mastermind of Benghazi attack

I'm guessing if somebody kills Americans in a terrorist attack on the US embassy in Paris he will be tried in a French court for crimes under French law.

How does a US federal court have jurisdiction, here?

The trial is being held in US district court in Washington – a civilian federal court – at a time when the Trump administration has said terror suspects are better sent to the military prison at Guantánamo Bay, Cuba.

. . . .

He has pleaded not guilty to the charges, including murder of an internationally protected person, providing material support to terrorists and destroying US property while causing death. 

. . . .

[Assistant US attorney John] Crabb said the prosecution would show the jury videos of the attack site and Abu Khattala’s phone records, which he said showed a spike in activity during the attacks. 

He said witnesses would include weapons and fire experts and a man named Ali, who was paid $7m to befriend Abu Khattala and help US forces capture him in Libya.

After he was captured, he was taken to a US navy ship that transported him to the United States. 

During the voyage, he was first interrogated by intelligence personnel and then by FBI agents. 

Crabb said Abu Khattala told FBI agents that America was the “root of all the world’s problems”.