There are downsides to achieving fame through a fashionable television series. People in supermarkets confuse you with your character. Those tabloids catch you in the least flattering postures. But it’s not all intrusion and inconvenience. Among the less celebrated advantages is the ability to help get lower-budget features into production.

This is not to suggest that Rob and Ronan Burke's Standby wouldn't have made it into cinemas without Jessica Paré on board, but the presence of the French-Canadian actor – best known as the second Mrs Don Draper in Mad Men – certainly helped the Irish feature surge forward.

“It’s a wonderful position to be in,” she enthuses. “It’s so often out of your hands in this profession. I am still a bit surprised by all this. So, I am happy to be of service. It’s very hard to make any sort of film in the current climate.”

Standby stars Paré and Brian Gleeson as, respectively, a glamorous illustrator and an underachieving airport employee, rekindling an old romance on the streets of Dublin. Paré seems magnificently foreign. We may all be frightfully cosmopolitan now, but the hint of Québécois adds exotic colours as she flits through Temple Bar.

Along the way she gets a chance to do great things with a Hank Williams number. Remembering her rendition of saucy French number Zou Bisou Bisou in an episode of Mad Men, we might reasonably ask if she ever thought of becoming a singer.

“That is very, very kind of you,” she says in a patient voice. “I loved to sing, but, until now, that has been mainly in the shower and in traffic. But if there’s a career path that’s trickier than acting, it’s music. So, I don’t know if that’s an amazing back-up plan. The character isn’t supposed to be a great singer. So, it’s all right.”

Yet, she has performed for thousands. I had read that, a few years back, she appeared on stage with The Jesus and Mary Chain. The Scottish band are, apparently, pals with her boyfriend, the musician John Kastner.

"Yes, William and Jim [Reid] are also fans of Mad Men," she says. (Really?) "I just lucked out on three or four of the tour dates. That really was terrifying. You know they're somebody's favourite band. They've got a babysitter. They've bought drinks. So, you really can't muck it up."

Draper parallels

There are parallels between Jessica Paré and Megan Draper (née Calvet), the character she plays in Mad Men.

As she points out, Megan is not a very French name, so it’s fair to assume Matt Weiner, the show’s creator, made her a French-Canadian only after they’d cast Jessica. Both actress and character have an academic for a father. Paré’s dad was chair of the education department at McGill University.

“That part is a coincidence,” she says. “I really don’t think they were thinking of me when they wrote that. But Matt loves Montreal. He loves all that French-Canadian stuff.”

Megan begins as a secretary, gets a chance to write some copy and then, terrifyingly suddenly, finds herself married to advertising existentialist Don Draper. Was it a surprise for Paré? Did she sign on for a supporting role?

“Pretty much,” she says. “I didn’t even know I was going to be a secretary. There wasn’t much written for her. But I guess that they had it in their heads that she would become the next Mrs Draper. I had no clue at all. I just thought I’d be in a few episodes.”

So, did she first realise when she read the script?

“Almost. Matthew phoned me and said in the next episode Megan is going to get married to Don Draper. He got me when I was in the middle of a nap. So, I was afraid I might be dreaming. The next day somebody came in and measured my finger for the ring. That was very fitting.”

After eight years and seven series, Mad Men is finally weaving itself towards a conclusion. The fired-up turbulent 1960s are oozing into the cynical, seedy 1970s. Next spring, the second half of the bifurcated final season will either reveal all, or, more likely, tease us with some cunningly ambiguous final conundrum.

One imagines Jessica Paré’s friends are constantly badgering her for spoilers.

“People ask me but I don’t think they really want to know,” she laughs. “If I were them I wouldn’t want to have it ruined for me. You can’t meet somebody from a show you like and not ask them what happens. But you don’t really want to know.”