It happened in Angelo's, one of the few little indie cafes left in downtown LA. I amble over there most days for the bubble tea or, if it's winter and I'm feeling particularly old-fashioned, the cappuccino. The exterior isn't too exciting – there's the ubiquitous Mr Cluck's Chicken on the opposite side of the road, offering ten times the space and twenty times the portion size of Angelo's, while to the right there's a Turkish supermarket and to the left a self-proclaimed bookshop, though it contains none of the paper that I persist in maintaining – to the annoyance of my grandchildren – to be an essential component of a book. The inside, however, is extremely welcoming. Armchairs, a familiar but not overly familiar barista, a selection of magazines and newspapers in mercifully non-electronic format. And you've got to support these independent places.

I'm an American. I like individuality. If I wanted to go and sit in a pastel-coloured plastic-covered vacuum and drink dyed water, I'd sign up for the local kindergarten. So, in that vein, even the disquieting print in the far corner of Caravaggio's David with the Head of Goliath is a comforting sign of eccentricity. You'd never find something like that in Espresso Universe. Admittedly, I could live without the wallpaper – arsenic green, is the most apt description I've heard.

Anyway, I'm rambling. I just wanted to fill you in on the details. The devil is, as people used to say, in the detail.

The cappuccino had arrived at my usual table. The café was packed and noisy – that never bothers me. I've always been able immerse myself in whatever I'm reading, which in this case was the culture supplement to that day's paper. Besides, these days, now that I live alone, I can frankly admit that I enjoy the racket. Some of the best times of my life have been spent surrounded by the patterned chaos of many voices speaking at once. When my daughter took the kids to stay with us, for instance, one Easter back in the sixties.

Excuse me, this voice said as Act IV from Le nozze di Figaro began on the radio. And again, louder, excuse me, because it took me a while to realise the voice was real and speaking to me. You know how it is when you're reading. I looked up, and saw a figure hovering round the only free chair in the room, and the only free chair happened to be at my table.

I said nothing, just signalled with a hand that this person should sit. Thinking no more of them, I returned my attention to the reviews. Yasmin would have immediately started to chat, but I've never been into coffee shop friendships; the odds of having something in common are so low and the chances of being bored to death so high that they've never seemed worth the trouble.

The theatre, film and music reviews were devoid of interest that day. Ultra-modern expressionism competed with neo-realist revisions of Beijing opera. Not my thing at all. The exhibitions page was more promising. At the Getty, there was a collection of manuscripts, letters and art connected to Samuel Taylor Coleridge, while the CIA was opening part of its Rambaldi archive to the general public for the first time in years, if not in decades. The facing page had a big colour print of a Byzantine-styled gold box; stark against the black background, glowing under a single weak spotlight, it looked quite dramatic.

I leaned in my chair back, considering whether my granddaughter might like to go to one and, if so, which. The Rambaldi seemed more likely to grab her attention. She's always been a smart kid, but not what you'd call bookish. And besides, everyone likes a bit of Renaissance bling. Even retired professors of literature.

On the sidewalk outside the window, a young couple were strolling past, arm-in-arm. They were an unlikely pair: the man rather stiff and dull in a grey suit, the girl a vision of Pre-Raphaelite loveliness with chestnut hair curling down to the small of her back. When they paused and, turning to each other, shared a deep kiss, her hand coming to rest underneath his shirt, I averted my gaze. It landed on the less romantic if still peculiar figure sitting opposite me.

Although the sun was blazing onto his head and side, he made no attempt to move his chair a few inches into the shade. He appeared not to feel the heat. Since my recent illness, I've become overly sensitive to the cold – the first sign of approaching senility, I suspect – and yet today, even I was wearing a t-shirt. This man, perhaps a decade or so younger than me, was wearing a jacket over a thick polo-neck, which, taken together with the half-grown beard and tinted glasses, suggested that he'd strayed into my café from winter on the Montmartre without stopping to change. I noticed that he was reading the same paper as me, open on the same page. Despite my reservations, I decided to speak.

'I can't decide. Both sound appealing.'

The stranger looked up inquiringly. I thought he might, like me, need time to adjust his mind from the page to the real world. But before I could nod at the paper in order to clarify my meaning, he replied.

'Ah, the Coleridge and the Rambaldi exhibits,' he said, removing his glasses and carefully tucking them into his jacket pocket. 'But you could go to both, surely?'

The trace of a French accent showed that my initial frivolous impression of him had been surprisingly accurate. Out on the street, hordes of young people were bounding along in almost Edenic states of undress, on their way to who-knew-what party or engagement; within, friends chatted and laughed over sugar-sweet drinks. We were the oldest in the café that afternoon, and we were both alone.

'I could – but my granddaughter is getting married next week. She'll just have time for one trip, at most.'

'Ah –félicitations!' he said amiably. I forced myself to grin. After the wedding, she would be going on her honeymoon, and then to live in Baghdad with her new husband. I can't say I was looking forward to watching the Rolls drive away with them inside. 'My grandson has just started walking. I hope I live long enough to see his wedding.'

'He lives here in LA?'

'Alas, no. In Provence. As you may imagine, I can hardly wait for my business here to be concluded. I mean no offence to your city, Mr…?'

'Jack Bristow Vaughn,' I said, and then, because no one bothers with surnames on Saturdays: 'Jack.'

'Jean Briault.' He paused. 'Pardon me, but I think I know your name. It is familiar to me.'

I was expecting him to mention my mother. A few articles had been published about her towards the end of her life, and her death had unleashed a surge of obituaries and over-enthusiastic journalists. I actually caught one rooting around the trash outside my parents' house at midnight.

'There was a twentieth century spy. A Monsieur Jack Bristow of the American secret service. People say he shot Salvador Allende, the Chilean President.'

'No people that I know.' I was pleased that I kept my voice steady. The remark about Allende had struck from a clear sky; not knowing whether to be angry or amused, I added, 'My grandfather was a good man.'

Briault smiled. 'Mais oui. Of course he was. Everyone's grandfather was a good man.'

He rested his chin on his clasped hands. For a few moments, I thought that was the end of our conversation. He seemed to have retreated into himself: his shoulders were hunched and his eyes were cast downwards. I forgave the Allende gaffe; he looked so withdrawn it was impossible not to.

I drank my coffee. As I put the cup down, I thought of my namesake. Briefly, after Mom died, I had toyed with the idea of writing his biography. But the official-looking photo of him that I'd been familiar with since childhood looked so severe, so disapproving: it was no great stretch of the imagination to picture his reaction to the news that his grandson was digging up his secrets and offering them to the voyeuristic appetites of the general public. He had been betrayed so many times in his life. In death, I let him be.

'Your mother also was a famous agent.' Briault was speaking again. 'Famous all over the world. I think even in Mongolia, they have heard of Sydney Bristow. May I ask an impertinent question?'

Warily, I tried to read his expression, in order to gauge just how impertinent the question was likely to be. He had a mobile face; the deep lines on his forehead and round his mouth shifted frequently, apparently responding to a rapid flow of ideas and emotions. Unfortunately, the significance of those movements, if any, was lost on me. I couldn't tell whether he was motivated by harmless curiosity or by something meaner, and altogether lower.

I nodded in assent. 'Ask'.

'I do not think you are like your mother and grandfather. You were never tempted?'

'No. Never.'

'I find that hard to believe.'

'You know that my grandfather was Jack Bristow. Maybe you've heard what happened to him?'

He tilted his head, and gave me a look of measured interest. 'I assume he simply retired. Even old spies must retire one day.'

'No. He was shot. By his oldest friend. His wife betrayed him, and his friend murdered him.' I kept the heat I felt out of my voice. There were examples closer to home I could have picked. My father. Kathy. But I find it hard to speak their names aloud, and what happened to them was, after all, none of the Frenchman's damn business.

'It's hard to imagine…what a dreadful thing.' He sipped at his glass of water. It was a strange thing: he was sitting in a café in downtown Los Angeles, drinking only what he could have had at home for free. Catching my glance, he gestured at the packed tables. 'I appreciate the company.'

I could understand that.

'About my grandfather. That's er – probably still classified. I shouldn't have told you.' I snorted. 'Not that it matters to me. Once you get past seventy, most things lose their power to terrify.'

'Except threats to one's family,' said Briault mildly.

I stared at him. Something in his matter-of-fact delivery made me feel rather ill. 'Yes – of course – '

'But tell me – what happened to your grandfather was certainly tragic, but that didn't make your mother reconsider her career.'

I bridled, and immediately felt irritated with myself for feeling irritated. This man wasn't the first to imply that I was a coward or unpatriotic for staying well clear of the family tradition - if, indeed, he was implying any such thing. I am old enough to know when I have strayed into an area where raw emotion and insecurity cloud my judgement. I wheeled out my usual lie.

'I failed the entrance tests.'

Briault looked at me levelly, impassive. 'Did you,' was all that he said. It was not a question. He closed the newspaper, and stood up. 'It was a pleasure to meet you, Jack. A real pleasure,' he said, and briefly clasped my hand. His palm was cold. Far colder than it should have been, given the weather. When he let me go, I tried to recall whether it was customary for men in France to hold hands in parting. 'Have you decided?'

'I think she – my granddaughter – would prefer the Rambaldi. She loves puzzles. And gold. So putting them together sounds like a promising combination. I read something about a machine that had to be assembled out of four hundred separate pieces – and when it was assembled, a quill pen wrote a message on a length of parchment. Just one word -

'Peace,' said Briault, raising his eyebrows sardonically. 'I know. Assembling that device of his sounds like a lot of work to discover something you could learn from a –un biscuit chinois - from a 'fortune cookie'. Rambaldi's toys glitter very nicely, but are hardly worthy of more than a few minutes' consideration. But Coleridge: his work is for eternity.' The corners of his mouth twitched. 'Trust me.'

I watched him walk away. At the door he stopped, just long enough to replace his glasses. Then, putting his hands in his jacket pockets, he disappeared into the crowd.