Disney has cooked up a yummy batch of gumbo with this blend of the past and present. “The Princess and the Frog” is a satisfying and thoroughly entertaining return to the hand-drawn animation that built the studio. Although it is set in 1920’s New Orleans, it has a modern twist with the studio’s first African-American “princess” — and this is not a heroine who warbles about waiting for the prince to come and rescue her. This is a working woman and the prize she has her eyes on is not some happily-ever-after fairy tale wedding. She wants to run her own business — a restaurant. Like Gepetto, she wishes on a star, but as her father advises her, “that old star can take you only part of the way. You have to help it out with hard work of your own.”

We first see Tiana as a little girl, playing with a good-hearted but spoiled little girl named Charlotte. They enjoy listening to Tiana’s mother, Eudora (Oprah Winfrey) read them the story about the princess who kissed a frog and turned him back into a prince. But Charlotte is wealthy and Eudora is employed by her father (John Goodman) as a seamstress. Tiana’s family may have modest means, but her parents love her dearly and she shares her father’s passion for cooking that signature New Orleans dish, gumbo.

When she grows up, Tiana (Aniki Noni Rose of “Dreamgirls” and “The No. 1 Ladies Detective Agency”) is working hard, determined to make her father’s dream of a restaurant come true. (It is implied that he was killed in World War I.) So she works two jobs while her friends tease her about not having any fun.

Meanwhile, Prince Naveen (Bruno Campos of “Nip/Tuck”) arrives in town, hoping to marry a rich woman but much more interested in playing music and having fun. When he is turned into a frog by Voodoo villain Dr. Facilier (“Coraline’s Keith David), he must find a princess to break the spell. That does not include Tiana, even though she is dressed like a princess at Charlotte’s masquerade ball. He persuades her to kiss him by promising to give her the money she needs to get the building for the restaurant. Since she is not a princess, it goes wrong and she turns into a frog instead.

And that puts them on a journey through a swamp to find a way to become human again. At first the free-wheeling prince and the serious-minded would-be restaurateur have little in common. But soon, as they make new friends (a horn-blowing alligator named Lou and a brave firefly named Ray) and try to keep away from frog-hunters and other dangers, they discover that they get along. They inspire each other to be their best but they like each other for who they are. And that, it turns out, is the real magic.

There is some real Disney animation magic in the details of the settings, especially the jaunty New Orleans of the Roaring 20’s and a musical number in the swamp with fireflies that is heart-stoppingly lyrical. The lively score by Randy Newman pays tribute to the vitality of New Orleans influences, with some zydeco spiciness, but there is sweetness as well, especially when she sings about her dream for the restaurant and imagines what it will be like.

Because this is Disney’s first African-American princess, there has been some extra scrutiny and some extra sensitivity. Some have already been critical of the film because Tiana is not a “real” princess, because she spends a good bit of the story neither black nor white but green when she is a frog, and because her romantic interest is not African-American but from the fictional European country of Moldavia (Campos is from Brazil). There will also be criticism because of the voodoo (with some scary skeletal images) and SPOILER ALERT this is the first Disney film in my memory where one of the key sidekick characters is actually killed by the villain.

I like the fact that Tiana is not a “real” princess like Jasmine, Snow White, Sleeping Beauty, and Ariel. Like Belle, she is non-royal, but romantically involved with a prince. More important, she is an independent, self-supporting, hard-working woman with ambition that goes beyond some sort of romantic rescue. The movie lightly touches on but does not ignore the racism of the era. I like the inter-racial romance (and note that the only other loving couple is Tiana’s parents, both African-American, voiced by Winfrey and Terrance Howard). Setting the story in New Orleans, an exceptionally diverse city, and in the 1920’s, an era of great creative vibrancy, was an especially clever idea. As for spending most of the movie as a frog; well Mulan spent most of her movie as a man. Transformation is at the heart of fairy tales. And in her human form, Tiana is as lovely as any Disney character in history, without being squeezed into a wasp-waist and harem pants like Jasmine. I have some smallish quibbles with the voodoo villain and some overly complicated plot twists, and a more medium-sized quibble with the death of a character. Though it is handled with some grace, it is still unnecessary and likely to upset some younger audience members.

But the movie is genuinely enchanting and the old-fashioned, hand-drawn, 2D animation has a timeless quality that makes us feel welcome. It turns out you don’t need CGI and 3D to feel that you can almost smell that spicy gumbo.