HORNELL, N.Y.—The future of American high-speed rail is sitting in a building older than the Battle of Gettysburg: a cavernous factory that holds the first shells of a $2 billion fleet of Amtrak Acela trains due to begin running from Washington, D.C., to Boston two years from now.

Even as Congress moves toward renewed debates over the future of both Amtrak and high-speed rail, the first of 28 new Acela train sets are starting to take shape here. They are the first new generation of passenger trains on the railroad since the Acela’s debut in 2000.

For Amtrak, that means a chance to relaunch a service that has been both a commercial success and a procurement headache—and still the nearest approximation in the U.S. to the high-speed trains that whisk travelers among major cities in Europe and Asia.

Amtrak is buying 28 new sets of power cars and passenger coaches from French manufacturer Alstom SA, which is assembling the trains at its complex of plants in New York’s Southern Tier. The train model, known as Avelia Liberty, is from a family of trains already in use in France and Italy, Amtrak executives say.

The new trains will be slowly entering the existing Acela service and will have a top speed of 160 miles an hour, up from 150 miles an hour on the current fleet. The trains will be built to tilt up to 6.3 degrees, allowing trains to run faster in curves and save energy by avoiding braking for some turns.