The Constitution gives judges the authority to decide controversies between U.S. citizens and non citizens, but if no U.S. citizens are involved there is no rule what they can do.
I think the jurisdiction thing is based on geography. If a French national mugs a Chinese guy in Portland, he can still get tried in a US court.
Of course, IANAL, don’t play one on TV, didn’t stay in a Holiday Inn Express last night, and courts are constantly making rulings based on jurisdictions I don’t agree that they have, so YMMV.