There are about 4000 watery miles between Miami and Paris. But for Robyn Peterson, who grew up in sunny Florida, and moved to the French capital when she was 16 to launch her modelling career, the cities may as well have been a million miles apart. ‘I was used to seeing men in white shoes and gold chains. Miami Beach in the late 60s was full of nightclubs and small-time gangsters. I got to Paris, and it was a whole other world. I’d never seen anything so beautiful. I remember walking down the street and thinking, “oh my god almighty!” I couldn’t speak the language, I couldn’t understand a word. But it was an amazing experience.’

Now in her fifties, and chatting from her home in Los Angeles, Peterson rewinds the tape to when she was a blonde beanpole riding her bike around Miami. She was coming off the beach one afternoon when – in true lucky break style – Valentino just happened to spot her in her swimsuit. The 14-year-old was hired on the spot by the designer to appear in a charity fashion show. ‘I didn’t know what a fashion show was. I didn’t even own any make-up, so it was all pretty strange to me. But I think something went off in my teenage brain.’

For a restless teenager desperate to escape Miami, the opportunity to model and see the world was too much to pass up. After a brief stint in New York, she made the leap to France where she ended up working for Vogue, Elle and Marie Claire, with master photographers like Guy Bourdin and Helmut Newton. Her tale of local girl does good, where flip flops and school uniform were suddenly out, and stilettoes and haute couture in, is the subject of Catwalk Confidential. Part memoir, part behind-the-scenes peek at the fashion world, the play is Peterson’s account of the decade that she spent in Paris during the 1970s.

‘It’s a coming of age story about a girl who leaves Miami on the Greyhound bus,’ says Peterson of her one-woman show, which she wrote and stars in. Full of ‘sex, drugs and rock‘n’roll’, Peterson says it takes the audience through the highs and lows of a hazy, hippie era, where champagne flutes and hash pipes passed by in a blur, until the bubble finally burst. ‘It’s sort of like Eliza Doolittle meets Eve Harrington,’ Peterson explains, namedropping the fan who turns into a bitter rival of Bette Davis’ fading Broadway star in All About Eve. ‘She’s a fearless gal who meets a Prince Charming who gets her into modelling. She starts working pretty much right away in Paris and becomes one of the first American girls to hit France.’

After a whirlwind of catwalk shows for Dior or Chloé, and bare-bummed photo shoots for Vogue, Peterson’s salad days finally end when she meets every model’s nemesis: the younger girl. ‘Age wipes you out,’ Peterson says with a shrug and a ‘what you gonna do’ tone of voice. ‘That’s the one thing that brings a model down: ageing. You have an expiration date. Younger blondes get off the bus every day.’ So she decided to hang up her heels and move to New York to try acting instead. ‘I was 26 when I left. I fell out of love with Paris around the time I fell out of love with a man. I had to start all over again basically,’ she says, before adding with mock wistful regret, ‘all those years, when you should have been learning to do something, or marrying a doctor, or something.’

So does all this reminiscing in her play make her nostalgic for that time? ‘It’s funny. I don’t think the old days were better. I just know they were different. Making so much money for the first time was really exciting. Of course there were also some grisly moments, and they’re in the play too.’ Among the low points of her Paris years, where she lived with other models in a tiny hotel, she recalls a good friend committing suicide by throwing herself out the window. ‘She just couldn’t cope. There were girls getting pregnant, having their hearts broken, taking drugs.’ Describing the cocktail of acid, grass and cocaine doing the rounds back then, she stops herself mid-sentence to add in a faux-serious whisper. ‘I’ve got to tell you Claire, I inhaled. Often. And I was no virgin either.’

She hopes the play is an entertaining ride, showing some of the uglier sides of the fashion world, but with plenty laughs. ‘Being in a one-woman show is definitely a personal challenge. I’m trying to get the story across, but with a lot of comedy too. I want to have a good time while I’m up there.’ Her transition to acting was tough when she first started out, but after a stint at acting school, she began making inroads. Earning her colours on US shows like Three’s Company (the US version of Man About the House), Cheers, Miami Vice and LA Law, she graduated to film roles. Eagle-eyed viewers can spot Peterson as a salesgirl in Pretty Woman, and she also turned her delicate hand to playing Jack Nicholson’s wife in Blood and Wine, Gwyneth Paltrow’s obese mum in View from the Top and a sex-mad traveller alongside Gerard Depardieu in My Father the Hero.

Perhaps her finest hour, however, was her cameo episode in The Sopranos, playing Uncle Junior’s mistress of 16 years, Bobbi Sanfillipo. After blabbing a bedroom secret that could cause Junior to lose his reputation, she is ungraciously dumped, with a lemon meringue pie straight to her pretty little face. Peterson remembers the phone call, over a decade ago, about the part. ‘The casting agent called saying there might be a job. I said “sure, great! But, you know, I don’t take my clothes off anymore?” She said I might have to talk dirty. I said “oh god, I’m married now! But OK, I’ll think about it. Just send me the dirtiest page of the script”.’

Being the first series, Peterson, like everyone else, knew nothing about the show. ‘The minute I read the script I thought “oh wow, that is some show.” The writing was so spectacular. I had a fun time working on it.’ As for that pie in the face scene, they couldn’t do lots of takes, because it would mean redoing the make-up and changing the clothes. ‘So, Junior hit me in the face with the pie, pretty hard, and the pie tin wouldn’t come off. So I’m there trying to push the thing off my face with my tongue. It took a long time. I thought I might have to eat my way out of there.’

After Edinburgh, Peterson would love to take Catwalk Confidential to London, or home of her hippie heyday, Paris. She’s also working on a second play, but in the meantime would love to get a phone call from casting agents on a few of her favourite TV shows. ‘Something like In Treatment would be really great,’ she says, referring to the Gabriel Byrne-starring psychotherapy drama on HBO. ‘If Absolutely Fabulous ever got remade, that would be a lot of fun.’ While she dreams up possible career paths post-Fringe, the rational side of her brain is occupied with much more practical things.

‘Is it true you can’t wear high heels in Edinburgh?’, she asks, sounding slightly worried. ‘I’m gonna need to find some good flats for all those cobblestones.’ Spoken like a girl always destined for much bigger, better things than the land of the white slip-on shoe.

Catwalk Confidential, Assembly Hall, Mound Place, 0131 623 3030, 8–30 Aug (not 17, 24), 6.20pm, £9–£10. Previews 6&7 Aug, £5.