American Airlines, British Airways, and Iberia have round-trip flights from Dallas (DFW) to Helsinki, Amsterdam, Dublin, or Madrid (HEL, AMS, DUB, MAD) for $450-$455, NONSTOP or with connections. Flights in September-October. Very few extended weekends available.
Amsterdam is the most expensive in this list, with prices around $570. Other destinations have prices in the $450-$480 range.
Madrid has limited availability.
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.