There’s a languid, romantic sweep to “An American in Paris” that gives this old-fashioned musical a transporting dreaminess. The show’s combination of lyrical, old-fashioned music — composed in the 1920s and ’30s by George Gershwin with lyrics by his brother Ira — and the elegant ballet choreography of director Christopher Wheeldon makes it feel like we’ve been teleported into an escapist fantasia.

You would want to hang out in a world of dance and beauty, too, if you had suffered through the experiences of the characters in this Tony-winning show, whose national tour is playing the Ordway through Sunday.

“An American in Paris” is billed as “a new musical” but its source material and style are classic Broadway, repurposed for the beloved 1951 Gene Kelly movie and now returned to the stage with a book by writer/director Craig Lucas.

The action is set in the wake of World War II, which left Europe in ruins. The ravages of war are not represented visually in “American in Paris,” whose gorgeous design features projections of tidy Parisian streets and cafes as well as neat set pieces that are whipped on and off stage by fleet-footed dancers. (The scenography, by Bob Crowley, draws heavily on French masters.) But there’s a hint of traumatic experience in the back story of Lise Dassin (Sara Esty), a French ballerina who sheds her shyness when she’s dancing.

Lise is the object of fevered desire by smitten Americans Adam Hochberg (Etai Benson), a G.I. with a bum leg who has stayed behind in France to pursue a career as a composer, and ex-Lt. Jerry Mulligan (McGee Maddox), who is a painter.

Both want to win Lise’s heart, or at least capture her in their art. But Lise is betrothed to the scion of a textile merchant. And Jerry is being pursued by a rich and lusty American heiress (Emily Ferranti).

The tour orchestra, conducted by David Andrews Rogers, gives the Gershwin score a sweet, soulful fullness. It is easy to be captured by these tunes, which fit hand in glove with the clean, graceful choreography.

The cast is mixed. Esty, who alternates the lead female role with her twin sister, is a fluid performer who’s magnetic as both a dancer and actor. As her partner, Maddox is a stronger actor than dancer.

Benson, as the narrator and pianist, delivers with charm in a show that is all about running away from reality, and all about the heart. Sometimes, that’s what people who have come through horror must do.