When Israel Horovitz was 13, he submitted a novel titled Steinberg, Sex and the Saint to Simon & Schuster. The manuscript was rejected with a letter - penned by someone who didn't know the aspiring author's age - praising its "wonderful childlike quality". That was "the unkindest cut", says Horovitz, laughing down the line from a hotel in Orlando, Florida.

Undeterred by this early setback, the son of a Massachusetts truck driver went on to become one of modern theatre's most prolific and performed playwrights. Asked whether writing was a compulsion, Horovitz says no; he saw it "as a way out of town". "I think if I had been unable to be a writer, if I had been unable to express myself that way, I might have been in jail right now. But thank the Lord I found that at a really early age."

We are talking because, having had "more than 70 plays produced around the planet", Horovitz has now turned one of them - the popular, Paris-based chamber piece My Old Lady - into a film, placing him in the director's chair (in cinema, at least) for the first time. "I needed to do something to scare me".

My Old Lady was conceived as a love letter to France. However, there wasn't much of the city in the play and he saw an opportunity to put this right on screen. The result is a blackly-comic drama in which family secrets burst into the open after an American deadbeat (Kevin Kline) inherits a Paris apartment from the father he blames for his problems, only to discover he must pay a monthly sum to the old lady (Dame Maggie Smith) living there with her daughter (Kristen Scott-Thomas), until she dies.

The play included numerous references to the Nazi occupation of Paris and France's treatment of the Jews, but these have been left out of the film to sharpen its thematic focus. Horovitz, who was awarded the French insignia of Commander of the Order of Arts and Letters, in 2012, admits, though, to being disturbed by the resurgence of antisemitism in the country.

"It's confusing because when I am in Paris I don't see a drop of it. I have been Israel Horovitz for a long time and no one is going to come up and make some terrible antisemitic remark to me," he says. "But I have a television and I see the marches on the street. It's not like there are millions of people parading with Hitler salutes but there are hundreds, and I don't see thousands running to stop it. . . I have very intelligent, powerful Jewish friends who are horrified and talking about leaving France."

Born in 1939, Horovitz grew up in the "white little Protestant town" of Wakefield, Massachusetts. "I would hear, almost on a daily basis, somebody say, in some form, 'Why did we not just give the Jews to Hitler? Why did we lose all our American boys?' That's the town I grew up in. Now there's a synagogue in town."

If the world outside his home could be cruel, inside it could be tough, too. Horovitz's father was an "unhappy guy". He wanted to be a lawyer but had been forced to leave law school early. After driving trucks for years, he achieved his dream at the age of 50. "He was really violent," says Horovitz. "As a child, I thought my role in life was to run between my mother and father when they were having a violent argument, and deflect my father's anger so he wouldn't kill my mother." His father changed after becoming a lawyer but "it was too late", says Horovitz. "I was already 16 and had one foot out of the door."

It is no exaggeration to say writing saved Horovitz. He cites, too, the support and encouragement of people like Samuel Beckett, who became a significant figure in his life.

I ask Horovitz if he ever thinks about his legacy. Not normally, he says. But today is different: just before I called, he and his wife had been watching the first cut of a documentary that a young French film-maker has been making about the writer for the past four years.

"I was sitting in this hotel room, playing the thing on my computer, with people giving testimony, and I was sobbing. Absolutely sobbing."

He didn't know how it would turn out when the director came to him, because she "was just a kid with a camera" and so he was generous with his advice. His voice cracking with emotion, Horovitz adds: "I guess you could marry that to my knowing how important it would have been to have somebody put his arm around me and say, 'Yes, you can do that. You can be a playwright.' And Beckett did that with me. And Thornton Wilder did that with me. And my high-school English teacher. In a kid's life, this can be a life-jacket that keeps you afloat. It's amazing the responsibility we old ones have."