HiCustomer and welcome back to JustAnswer!
I'm assuming DFW is Dallas/Fort Worth, and this is where you will be departing.
Usually, the best day of the week to book the least expensive flight is Wednesday.
After Wednesday, the best days to book departures/arrivals are Tuesday and Saturday. Very often, airlines have cheaper airfares that are only good on Tuesdays, Wednesdays and Saturdays.
The least expensive time to fly is typically the first flight out in the morning. The next best times, price-wise, are flights during and/or after lunch and flights at the dinner hour. You can see more information re: how to get the best airfares and when to book flights, here:
This site deals exclusively with travel tips to Europe:
You've already done the best thing in planning your travel for the last week in May, as this is considered the least expensive time to fly to Europe.
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Edited by Cher on 1/31/2010 at 10:13 PM EST