Two weeks after christening the largest container ship ever to visit a U.S. port, French shipping giant CMA CGM SA said it would use six of the behemoths on a regular service rotation between Asia and the U.S.

The carrier announced on Thursday that starting at the end of May, it will use the new vessels, each with a capacity of 18,000 twenty-foot equivalent units, or TEUs, on its Pearl River Express line, which runs from Fuqing, China to the U.S. West Coast, calling at the ports of Oakland and Long Beach, Calif., before returning to China.

Currently, the Pearl River Express line is served by seven ships, six of them with a capacity of 11,388 TEUs, and the CMA CGM Benjamin Franklin, the 17,859-TEU ship that was christened last month in Long Beach. The new ships that will replace the smaller vessels all bear the names of famous explorers.

“The decision is in line with both the growth strategy set by the Group in the United States and around the world and the optimization of its fleet,” the company said in a statement.

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Putting new vessels—particularly some of the largest container ships ever built—into service today puts CMA CGM at odds with other large steamship lines, which generally have been curtailing service amid a capacity glut and plummeting shipping rates.

Drewry Shipping Consultants Ltd., a London-based maritime research firm, said in January that losses in the container shipping sector could widen to $5 billion in 2016 amid falling freight rates. Ocean freight rates fell 9% in 2015, and rates on major trade lanes, particularly those between Asia and Europe, are at their lowest since 2009.

At the same time, shipping lines still are adding carrying capacity—1.7 million TEUs last year alone—as shipbuilders deliver ever-large vessels that were ordered over the last five years.

Shipping lines have been gradually increasing the size of vessels for decades, taking advantage of improving technology and engineering to reduce fuel and labor costs. U.S. ports, meanwhile, have struggled to keep up with the growing size of the ships, spending billions to deepen harbors, raise bridges and improve onshore infrastructure like roads and rail connections.

Jock O’Connell, an international trade economist affiliated with Beacon Economics, said CMA CGM’s move to integrate the new ships into its trans-Pacific service so rapidly was a surprise. The Benjamin Franklin made calls at several West Coast ports in recent months that appeared to be test runs of the ability of the ports to handle the ships.

“ They seem to have become obsessed with larger vessels without understanding the growth potential of the markets they are intended to serve. ” — Jock O’Connell, international trade economist.

Because of the decline of the volume in trade between Asia and Europe, for which these vessels were designed, they have to find some new way to use them, even though they’re still not quite sure that the West Coast ports can handle the surges in cargo that these big vessels bring with them,” Mr. O’Connell said.

He said that there was a “strong likelihood” the new, larger ships would lead to more overcapacity and send rates lower.

“I’m not sure there’s much sense in what’s been happening in the shipping industry in the last few years. They seem to have become obsessed with larger and larger vessels and economies of scale without understanding the growth potential of the markets they are intended to serve,” Mr. O’Connell said.

“It’s as if the maritime shipping side of things has become totally unhinged from the rest of the supply chain…No shipping line executive wants to admit to a mistake like that.”

Write to Robbie Whelan at robbie.whelan@wsj.com