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Both Delta and American Airlines via Skyscanner have round trip airfares travelling from Dallas (DFW) to Barcelona Spain (BCN) for $ 474, making 1 stop. These are basic economy fares but on both airlines, you are allowed a carry-on bag in addition to a small personal item for free. There’s an option to upgrade to the next fare level if you want.

Travel Availability:

Departs DFW: April 1, 6-7, 13-30; May 1-13
Returns: wide and great availability returns