Delta, Virgin Atlantic, and Air France have round-trip flights from Dallas (DFW) to Amsterdam or Madrid (AMS, MAD) for $524-$578 with a connection. Flights December, January, February, March, April, May, August, September, October, and November. Extended weekends available. Holiday blackouts.
A Carry-on bag and also a personal item is allowed for free on Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.