It is unusual that I can mention a favourite record and watch a wave of recognition cross my friends' faces. Not since my teens have I had to kick myself for missing Top of the Pops. Such is the lot of the jazz fan. Rarely,too, have I anticipated a concert as much as the Fringe show I attended this summer ­ and never before has my review been reprinted in a news story. Yet all these things happened this year because of one unusual singer and guitarist ­ Madeleine Peyroux.

Peyroux, for anyone who hasn't yet heard Careless Love, her beguiling album, or read the news stories about her supposed disappearance just as she hit No 7 in the charts, is a 32-year-old American who was discovered busking in 1996. She landed a record deal, released the well-received Dreamland, and disappeared only to resurface last winter with a "comeback" album that made her the most talked-about singer of 2005.

With her languid yet fragile vocals, which bear a startling resemblance to Billie Holiday¹s, and the unusual, folksy feel of her music, Peyroux seemed to be a throwback to an earlier, less commercial era. Add to the mix her self-imposed withdrawal from the public eye and her ongoing love of busking, and she appeared to be the real deal: a musician for whom making music, not fame and fortune, was the main motivation. Peyroux, a quirky character who ran off with street musicians in Paris as a teenager and threw away her first chance at fame when she realised "it wasn¹t really something I could handle", had an authentic air about her. When I interviewed her, back in June, I found her easy to chat with, as we shared interests in old movies (Mr Smith Goes to Washington is one of her favourites, though she struggled to remember its title), classic jazz (she loves Fats Waller and, of course, Billie Holiday) and Paris. Perhaps she was a little unfocused, but her southern drawl and pauses to smoke seemed to explain the laid-back pace of her speech, and her slow responses to questions.

After the interview, I happened upon a story about her ex-lover and musical partner, harmonica player William Galison, with whom she is embroiled in a legal wrangle over a CD. Got You On My Mind, recorded in 2003 (and guest-starring Carly Simon), has been dismissed as a demo by Peyroux¹s record company, Rounder Records. They have accused Galison of trying to cash in on Peyroux¹s success, and have threatened anyone who distributes it with legal action. This was the first inkling I had that all was not as Ms Peyroux¹s "people" at Universal, which has leased the CD from Rounder Records, had suggested. Peyroux herself had told me that she had had several abandoned attempts at a second record during the seven-year period which her press people cloak in a veil of mystery. Galison, who has alluded in his legal correspondence to her "history of attempted suicide", met her when she was playing in a New York bar in 2002, and she popped up as a sideman to the trumpeter Peter Ecklund on his CD Gigs, on the Arbors label. So, if she was really lost, it was only because nobody was looking for her. For Peyroux¹s Scottish debut at the Fringe in August, I invited along a jazz musician who had played on the same Ecklund session, and who was intrigued by the young singer¹s sudden celebrity. Neither of us could believe what we heard that night.

It was excruciating. Our jaws dropped as we struggled to reconcile the strangulated sounds from the stage with the sublime singing on the CDs. Madeleine Peyroux the live performer sounded like a tone-deaf geriatric warbling along with Careless Love. As my companion put it: "Her voice falls somewhere in that magical place between a dying Billie Holiday and Mr Bean." She sang flat, and out of time. Most of the songs were only recognisable because of the lyrics.

Peyroux seemed far from comfortable in the limelight. She stood awkwardly, going over on one ankle like a bashful child forced to perform in front of adults. Sometimes she turned her back to the audience. Her face was contorted as she sang and her pained expression, combined with her unsteady stance, was reminiscent of a drunk on the verge of toppling over. Between numbers, she laughed to herself and mumbled inanely.

Given what we witnessed, the only possible explanation we could come up with for Peyroux¹s success was the wonder of the computer programmes that are routinely used to transform poor singers into tuneful ones.

A fortnight later, news stories reported Peyroux¹s sudden "disappearance". Universal announced that it was hiring a private eye to track her down. An impressive amount of newspaper coverage later, Peyroux was found, at home in New York. Universal was accused of planting a hoax story to portray Peroux as the Greta Garbo of jazz, turning her reluctance to co-operate with media interest to its advantage. On the eve of a recent benefit concert for the victims of Hurricane Katrina she told The Herald¹s John Williamson: "A lot of things happened after my first album but I never disappeared. I had trouble with my voice and had to have an operation. We started to make a record and I was a little disappointed that we didn¹t finish it, and then there were things with the record company." However, the image of a diva falling for her own publicity seemed to be confirmed by her walking off the Michael Parkinson television show in March, after she refused to meet the producers¹ requests for a cheery, Saturday-night-style song. Although the girl who wistfully described to me her days on the "acoustic streets" of Paris didn¹t seem remotely diva- like, a contact who has worked with her shared my suspicion that she had become something of a liability to her record company. "She¹s just not hungry for success. She got where she is by default and thinks it¹s all a bit of a joke. For her concert at the Queen Elizabeth Hall, she pulled a crumpled skirt out of a plastic bag. I think she would be just as happy singing her songs in her bedroom."

Maybe the truth of the Parky affair is that the silver-haired presenter had heard Peyroux live and, like me, had been horrified by the difference between the voice he loved on disc and the voice that confronted him in his studio. Whatever happened, the incident also cost Peyroux ­ or her publicity people ­ a high-profile gig at Parkie¹s pub. "The thing that is strange about that stuff," she says, "is that I haven¹t been anywhere. I have toured all year, and probably never been more visible. Even before the record came out, we went out on tour as a warm- up act to get me back into these types of show. "We have had great times and done some great shows," she told Williamson, "and there have also been some terrible ones. It can be a number of things ­ something that happens behind the scenes or just a disconnection between the stage and the audience. But right from the start, when the record came out, we had a lot of support in Europe. People there just seemed to get what we were doing faster."

The website www.madeleinepeyroux.org includes postings from as many deeply disappointed concert-goers (people walked out on her recent Amsterdam gig, and speculated whether she had spent too much time in the local cafes) as reviews from enthusiastic critics. If her live singing was as spellbinding as her CD suggests, Peyroux¹s eccentric behaviour would surely increase her appeal as a delightful oddball and an authentic jazz character ­ the (im)perfect antidote to the swathes of shiny manufactured jazz chanteuses.

Perhaps, though, she is a troubled young woman who is not equipped emotionally for the kind of attention she¹s been receiving, who can¹t be relied upon to produce the goods, and whose career is not her own anymore.

She told me that she¹d have to rethink things if she found herself being booked into seriously big venues ­ and now she¹s playing 2000-seaters. Maybe she'll have a good night in Glasgow this week. If not, there¹s still Careless Love ­ a wonderful recording by a singer who may not exist in real life.