American Airlines, British Airways, Air Canada, Swiss and various other airlines have round-trip flights from Dallas (DFW) to Zurich (ZRH) for $460-$475 with a connection. Flights October to March. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.