By Deepa Babington

FLORENCE, Italy (Reuters) - New York-based designer Diane von Furstenberg sent models traipsing down a lush garden runway in breezy chiffon dresses and ruffled headbands to mark her first fashion show in her native Europe.

Returning to the region that produced the first "wrap" dress that made her famous and courting European customers while the dollar struggles against the euro, Furstenberg showed off her pre-spring collection of travel wear in an open-air gala in a manicured garden tucked away in the Renaissance city.

"I do sell in Europe and have shops everywhere and but it just so happened that they invited me and I accepted and after I accepted I thought, this makes sense, this is where it started," von Furstenberg told Reuters.

"Going back to Florence was a very nostalgic thing for me. My first factory was 25 km from here, and the wrap dress was invented here," she said.

The Belgian-born designer had models bounce down the catwalk in flirty black and white sundresses paired with chunky brown or gold heels, while oversized bows and satiny headbands added to the girlish look.

Flowy dresses in bold geometric patterns splashed with sunflower yellow and engine red draped over the body like a sarong, while colour ran amok on one number that featured bold stripes of pink, ocean blue, red and white.

"It's not winter, it's not spring, it's transitional and it's nice, easy pieces, and season-less," said von Furstenberg, who became a princess after her marriage to Prince Egon von Furstenberg, which has since ended.

She is now married to media mogul Barry Diller.

Raised largely in Europe, von Furstenberg rose to fame in the 1970s with her hallmark wrap dress that became popular as a sexy yet comfortable option for women of all sizes.

The style is enjoying a revival of sorts lately, but that was not enough to make it the star of the show.

Tea roses, ribbon and ruffles dressed up classic halters and cocktail dresses, while shirt dresses were pulled together at the waist with skinny belts for a more feminine look. Cigarette pant-like capris and a classic beige trench coat cinched at the waist were tossed in to complete the suitcase line-up.

Evenings meant a shimmery white dress with a black belt, while a dark blue sheath dress with an off-the-shoulder twist set the mood for elegance to follow daytime chiffon and jersey knits.

Held before an adoring audience of Florence glitterati, Von Furstenberg's show kicked off the city's twice-a-year Pitti menswear fashion shows. They precede Milan's menswear shows that start Saturday and feature top names like Armani and Versace.

(Editing by Jon Boyle)