There is a man outside, doing something to the windows of Fiona Shaw’s house in London, and he appears to be following her from room to room. No sooner has she laughed, apologised, picked up her laptop (we’re speaking on Zoom) and sought peace elsewhere than – scrape, tap – the top of a ladder appears again, and his face looms behind her.

No wonder. I feel like following Shaw around everywhere too. She is such fun, bracing company. She can swing from references to Freud to word-perfect renditions of Yeats lines learned in childhood, and makes some lovely observations: describing lunch with Phoebe Waller-Bridge, she says the Fleabag creator is “like April or May. She’s blossoming on all fronts, all her fingers are light green.” Even the man working on Shaw’s windows is likened to something out of Rapunzel. She seems to delight in everything.

“I am as excited now as I was when I first left drama school and was having that marvellous time,” says Shaw. She has long been regarded as one of the most exciting stage actors of her generation, but in recent years Shaw has created a thriving TV career. In Killing Eve, she plays the ice-cool MI6 agent Carolyn Martens (she won a Bafta for it), and Waller-Bridge created the role of a therapist in the second series of Fleabag specially for her.

Shaw is in the second series of Baptiste, the spin-off series about French detective Julien Baptiste (played by Tchéky Karyo), who was first seen in the 2014 BBC drama The Missing. Shaw plays Emma Chambers, the British ambassador to Hungary. The character is similar to Carolyn, in that they’re both self-contained, sharp and capable upper-middle-class English women (so brilliantly good at that is Shaw, that it feels strange to hear her talk in her smooth Irish accent). But, whereas Carolyn seems largely in control of her world, Emma is plunged into chaos after her husband and two sons go missing while they’re all on a skiing holiday.

Shaw liked that Emma “is not that good a parent. I think that’s good writing because it’s more interesting than [her being] a heroine. She’s a bit cold, a bit distanced and absorbed in work, and a little bit unknown by her children. Part of the emotional journey of it is that she discovers her own passion for her children. It’s not somebody standing in their powerful position, it’s the opposite, and that’s always good.”

The series flips between timelines, and by the end of the first episode, it’s clear Emma has been pushed to breaking point. “There’s irony, there’s hindsight. A lot of it is about failure. In northern Europe, where we work terribly hard all the time, I’m not sure it’s really about productivity, it’s maybe more about puritanism, because other countries seem to get stuff done and live much gentler lives. Emma is one of those people who is nearly always ‘on’, her entrails knotted with tension. She sorts things out all the time and then can’t sort [what happens to her family] out.”

I hesitate to bring it up, but there are inescapable similarities between Emma’s loss in Baptiste and the trauma endured by Shaw’s wife. Sonali Deraniyagala, an economist, lost her entire family – her two sons, her husband and her parents – in the 2004 tsunami. The couple met after Shaw had read Deraniyagala’s devastating memoir, Wave.

Did Deraniyagala’s unfathomable loss make Shaw think twice about taking on this part? “Yes,” she says straight away. After a long pause, she speaks very carefully: “I’m being delicate, on Sonali’s behalf. How can I explain it? I do live with somebody who has had huge tragedy in their life, perhaps the greatest tragedy of anybody [one has] ever met, really. So, of course, it’s there, but … one doesn’t mine one’s life in that way.” And, she points out, “I think what happened to Sonali is worse.”

There is grief, Shaw says, and then there is “catastrophic grief”. “We’re all going to have grief. But catastrophic grief has catastrophic effects on people. If Sonali teaches me anything, it is that the worst can happen. Instead of saying, ‘why me?’, it’s ‘why not me?’ She was very concerned, during the worst of the pandemic, [about] people’s cavalier belief that it wouldn’t affect them. Doctors who were having to treat people who had been careless was a source of concern, because we shouldn’t be putting anybody else in danger.”

Fiction, Shaw says, “is there to throw a light on to darkness. What I like about the Baptiste series is that it is pitiless. I’ve always felt that the Greeks got that correct. The Christian ethic still dominates in the west – that if you do good things then good things happen. But it just isn’t like that, it is random and it is terrifying.”

Shaw – charming and clever – would have made a good ambassador in real life. She has met quite a few, she says – Irish, mainly, since she is such a valued export and is regularly invited to things – and knows how tough it can be. “I think it’s a life of terrible disturbance. And I would have thought in the last two years, being a British ambassador in Europe must have been one of the most impossible jobs, where they have to at one minute be making allegiance with those countries, and then in the next, be dismantling the allegiance.” If a diplomat lives a peripatetic life, so does a working actor. “For a long time, I didn’t root myself,” says Shaw. “I was always away, and when I think back it makes me tired to think how ‘away’ I was.”

Shaw grew up in Cork, the second child of four, and the only girl. She loved poetry and would often win prizes for reciting it at school – “it was very empowering speaking language that was much bigger than myself,” she says. “My mother was such a huge personality at home that probably it was at school that I was more of a personality,” says Shaw, whose mother is now in her 90s. “But we were always performing poems or quoting, there was good conversation at the table and everyone was reading, but not in a self-conscious way. There was also a lot of rugby.”

Her father, an ophthalmic consultant, insisted she go to university; she studied philosophy but kept acting. “We’d go to these festivals and I would show off a lot,” she says, laughing. “Dreadful 1960s plays but brilliant parts.” When she was 21, she moved to the UK to attend Rada, and then she was off – first to the National Theatre, then the Royal Shakespeare Company.

Around the same time, she started appearing in film, making My Left Foot and Mountains on the Moon. Then, she says, “I got to Hollywood and they said: ‘You’re very old.’ I remember thinking, ‘Shit, that’s bad.’” She was 28. Her next film, Three Men and a Little Lady, in which she played a frumpy headteacher, “completely finished my film career,” she says, laughing.

It wasn’t a great hardship – she was cherished in theatre, which is where her passion was; the film world couldn’t see much past her comic turn as an English eccentric (though she returned, triumphant, as Petunia Dursley in the Harry Potter films). “I think maybe I also thought film was something to do with being pretty.” A raised eyebrow. “I mightn’t have been wrong, either. I didn’t want to go to that party where I wouldn’t be picked.” Their loss.

Shaw’s theatre work included a long collaboration with the director Deborah Warner – notably, Shaw played Richard II, and performed some of the meatiest roles there are, such as Hedda Gabler and Medea. In 2013, she was starring on Broadway in The Testament of Mary; she looked up and literally saw her name in lights. “I remember thinking that’s about as doiiinnng [she makes a gong-clashing sound] as you can get.” She smiles. “And feeling tired.”

A bit burnt out, she wanted “a new kind of challenge”, and started to direct operas, to more critical acclaim. Living a more settled life also allowed her to be available for television work, timed perfectly with the revolution that was happening in TV and the creation of better roles for older women. “Their function is not to be just mums,” says Shaw. “I’ve been sent some marvellous things from America recently, that I may or may not do, depending on whether we’re ever allowed to leave our country.” She is currently filming the Star Wars spin-off series Andor for Disney+, and then there’s the final series of Killing Eve.

Shaw has had, she says, “a marvellous rejuvenation, both in …” A short pause. “I don’t want to say the word ‘career’, because I don’t even think of it like that, but in adventure and in life.” She and Deraniyagala married in 2018. “My life with Sonali is so not what I expected, because I thought, [theatre] was my life and the price I paid for it was just to be in that,” she says. Deraniyagala teaches at Columbia University in New York, so the couple split their time between there, London, Ireland and Sri Lanka, where Deraniyagala was born.

Having never thought she’d get married, Shaw is now happily so. “It gets rid of a lot of possibilities,” she says, smiling. “I think I now realise that being unmarried, there’s always a cliff edge and you wonder when you’re going to fall off it. [Being married] I don’t feel any sense of chaos. I wonder whether I felt I needed the precariousness of possibility in order to act in the plays that I did.” She laughs. “That’s a rather pretentious way of saying something. I don’t know. But I’m very happy to relinquish it.”

• Baptiste is on BBC One on Sunday at 9pm.