Once upon a time, the radical political activist turned fitness guru would have excited a feeding frenzy among the entertainment and style journos, but she now stands in the shadow of her equally famous husband, Ted Turner, the founder of CNN. He is neither an Oscar winner nor ravishingly beautiful, but he is the one who really matters in this duo.
Commerce can now rival art for star value; Miss Fonda ruefully acknowledged as much, remarking that even as an actress she had had little idea of where much of the genius in her industry sat. It was only after getting involved with Ted and "the Wall Street boys" - and she nodded towards her husband with something approaching awe - that she had begun to understand that far from being a bunch of boring accountants, the creators of our new media industries are amongst the most inventive and creative people on the planet.
Turner, like many modern businessmen of his stamp, is not a bean-counter; he is a vision man, with big ideas about the world. The business is merely a means to help deliver the world he can see in his head.
The story of CNN is well known. Turner started a news business that everyone thought would fail, led it to world domination, and then sold it for billions. His good ol' boy style grates on some, but that didn't prevent virtually the whole of the UK's media establishment showing up at a glittering fireworks party to pay homage. There was one notable absentee - Rupert Murdoch, whom Turner loathes with passion - for this was a gathering of a new type of business leader, who may, for all Murdoch's brilliance, one day eclipse his kind.
In one corner stood Gerry Robinson, boss of Granada, who appeared in Labour's famous election broadcast to business; in another, Clive Hollick, the moneybags behind some of New Labour's think-tanks; and, casually threading his way through the throng was Srichand, the elder statesman of the Hinduja dynasty, even richer than Turner himself. He is a member of one of India's most socially conscious families, passionate about healing the social and spiritual divisions of the south Asian tribe.
One might name others who were not there - George Soros, who has turned much of his vast wealth to rescuing Eastern Europe; and perhaps Anita Roddick, who this week claimed victory for one of her many campaigns, the drive to stop cosmetics being tested on animals.
What is most interesting about these men and women is not that they have social consciences, or that they give money to good causes. Capitalists have done that for decades; the inter-war moguls recognised that a return to the extreme poverty and division presided over by the Romanovs would only provide fuel to revolution. Any amount spent on blunting the edge of that threat was an investment.
The new, left-wing capitalists have precisely the opposite agenda. They are all fearsomely clever people who could probably make, in any number of ways, more money than they could ever spend; but it is becoming clear that they run businesses because they want the world to change.
In short, old capitalism ventured into social affairs in order to protect its business agenda; new capitalism runs businesses in order to advance its social agenda. And this is more than just handing out a few bob, though Turner's billion-dollar commitment to the UN is astonishing in itself.
Listen to them talking, and you hear men and women who regard profit and loss not as ends in themselves, but as tools to realise a world vision. It is no accident that many of them had their formation in the late Sixties and early Seventies, when Jane Fonda was politically active; they grew up believing that the world could be changed for the better by the action of people of vision and determination. Their heroes were not Ford or Hearst, but Kennedy, King and Mandela.
It is also no accident that so many of them are involved in new technology, media and services. Not only are these the fastest-growing sectors; they are also the businesses that allow you the chance to communicate basic values. An oil well or a steel factory may generate the cash to allow to be generous to charity; but computer software, films and television also allow you to put your vision of the world directly to the consumer.
In the US, Gates and Turner can hardly open their mouths without sounding the echo of McLuhan's global village. Domestically, Pearson's Greg Dyke and Scottish TV's Gus Macdonald started their working lives as left-wing activists; it's no surprise to see the former popping up to put the NHS to rights, and the latter virtually declaring Scotland a no-go area for English media companies.
The most articulate advocate of business as a form of political activism is probably Anita Roddick. She is a former teacher, and worked for a while at the International Labour Organisation. In an unreported speech she gave this week, she laid out in detail how she saw her business less as a means of satisfying the consumer and more as a way of engaging them with a defence of the environment and of human rights. It works, though no doubt her city backers could do without petitions in the shops, and the expensive but ethical purchasing policies that deprive them of even greater returns. Never mind; Ms Roddick seems to have captured the Zeitgeist of women in today's society, particularly the young. The money rolls in, irrespective of whether or not it helps the Ogoni people.
No wonder New Labour is so enthusiastic about business. Some of the most active exponents of Blairite values are precisely the sort of people who would have been the object of ritual attack in any self-respecting left-wing gathering 10 years ago. Yet today, it is people such as Clive Hollick, Greg Dyke and Anita Roddick who are most passionate about Labour's agenda for equality and social inclusion; and these men and women put their money where their mouths are; it is the left-wing capitalists who are most impatient with what they see as Labour's temporising on the social justice elements of The Project.
However, we should also feel uneasy. We may grow to love left-wing capitalism, with its commitment to equal opportunity, the environment, international friendship, and all that good stuff. But governments have a role, too. Globalisation has transformed these men and women into something new. Unlike the old capitalists, today's major businesses operate across the globe, and owe no loyalty to any one government. The brilliant stars of 21st-century commerce will be above the reach of governments; Bill Gates, Rupert Murdoch, Ted Turner sit with prime ministers and presidents, and neither they nor anyone else is sure who holds the reins of power; no one can say who really is the supplicant.
The left-wing capitalist may be a democrat and a liberator. He or she may well be the most creative force on earth, dedicated to shaping a better world. But are we in danger of allowing the globe to be their personal canvas, the media their own clay? And are we becoming actors on the stage of their dreams; and are our elected representatives simply mouthing their lines?