Flying to Europe in 2024 without spending a fortune is in the cards after a long stretch of sky-high prices.

Airlines have added new routes between the U.S. and Europe and announced plans to increase flights on some routes next spring and summer. The added capacity means travelers can get a break from the run of high airfares in the past couple of years. Some prices are still high—the average cost of round-trip airfare to Barcelona is over $1,000, according to travel-search website Kayak. But deals now exist that didn’t before, and industry watchers say they expect more to come.

“Everybody really wanted to go to Europe this past summer and pretty much everybody did,” says Kyle Potter, executive editor of travel blog Thrifty Traveler. “And they paid a lot to do it.”

Some airfares stand at or below prepandemic levels, according to a recent analysis of flight prices by Thrifty Traveler. A nonstop basic economy flight in early March from Boston to Dublin can cost as little as $433. You can find basic economy prices for flights from the U.S. to major cities such as Paris, Rome and Amsterdam for around $500 during that same period.

Booking premium seats with miles for flights next spring and summer also looks to be getting easier, Potter says, another sign of sagging demand.

And the cheaper seats aren’t just in coach. Thrifty Traveler found instances where trans-Atlantic business-class seats could be booked for under $2,000, including on JetBlue flights from Boston and New York’s Kennedy Airport to Dublin. That is about half what they cost last summer.

John Grant, chief analyst at travel data firm OAG, says fewer fliers are looking for premium cabins to Europe, a change from the revenge spending common in 2022. Grant attributes this to more fliers feeling economic turbulence.

Pick your spots

Prices aren’t universally low, but hunting for the best price now and in the coming months can pay off for trans-Atlantic travel next year.

A review of prices conducted last week by Thrifty Traveler found that it was possible to book round-trip flights to Barcelona from several cities in the U.S. for under $500 for flights on select dates now through May. Prices to Barcelona aren’t always that low. On average, the cost of flights to Barcelona next spring and summer is currently up 21% year-over-year to $1,043, according to data from Kayak. The Kayak analysis was based on advertised prices from the past month.

The current average cost of round-trip airfare to Europe is around $655, according to data from travel-booking company Hopper. Prices remain especially high for destinations in Southern Europe.

Airfares to Athens are up 22% year-over-year for travel between mid-March and the end of May, according to Kayak. Prices are also up by 20% or more for flights to Lisbon, Madrid and Milan.

Carriers are expanding the number of flights they operate across the Atlantic, which could ease prices, says Hayley Berg, lead economist at Hopper. Several low-cost carriers, including PLAY and Norse Atlantic, have started to fly between the U.S. and Europe in recent years.

Flying with a low-cost carrier often requires a layover in places such as Reykjavik in Iceland. These deals might be worth the added hassle. “I can imagine a lot worse airports,” says Kerry Tan, an associate professor of economics at Loyola University Maryland who studies airline pricing.

Many new nonstop routes set to launch in the coming months could lead to lower prices. United Airlines has grown its trans-Atlantic capacity by 30% since 2019, Chief Commercial Officer Andrew Nocella said during a call with analysts in October.

United will add a second daily flight between Newark, N.J., and Brussels in March and a second daily trip between Washington, D.C., and Rome in May, among other route expansions. The carrier is also starting its seasonal service to destinations in Southern Europe earlier than in previous years.

German airline Lufthansa is adding flights to Frankfurt out of Minneapolis and Raleigh-Durham, N.C., beginning in early June. JetBlue recently began selling tickets for flights next spring and summer from Boston to Dublin and from New York to Dublin and Edinburgh.

Bide your time

Knowing when to book your ticket is key to scoring a deal. Booking summer travel now may not be ideal.

“Airlines know that travelers booking that far in advance are either anxious or not flexible,” Berg says. She expects prices for spring and summer international flights to drop in the months ahead.

She suggests booking in January for spring trips and March for summer trips. Don’t wait too long, though—people who purchase summer flights to Europe in May likely will have to pay more, Berg says.

If travelers are agnostic about where they visit, open-ended searches for flights on sites such as Kayak or Google could turn up bargains. Otherwise, travelers should set up price alerts to track where prices are headed.

Knowing when to visit, and which places to avoid, also helps.

The Paris Olympics in late July and early August could have widespread spillover effects. Travelers may choose to visit France earlier in the year or go to other destinations to save money. Complicating matters is the fact that Paris is a major hub for connecting flights to destinations across the continent.

The influx of travelers to France for the Olympics could limit the options for people traveling to further-flung European destinations, says Kevin R. Williams, an associate professor of economics at Yale School of Management. Nonstop flights to Paris from the U.S. in late July currently cost anywhere from $600 to $1,000.

“That is going to be a more expensive ticket,” Williams says.

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Write to Jacob Passy at jacob.passy@wsj.com