American Airlines, Finnair, and Iberia have round-trip flights from Dallas (DFW) to Paris, Madrid, or Rome (CDG, MAD, FCO) for $501-$539, NONSTOP. Flights January to March. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required.
Rome has limited dates available.
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.