Alba and her mother, a good friend of Beckett's, will attend the Happy Days International Beckett Festival on Saturday and Sunday and read extracts from their own books.
As a young child Alba, by her own admission, did not fully grasp just how influential her parents' close friend was on the literary and arts world.
But now fully aware of her god-father's talent, she says she will take great pride in playing her part at the world's first ever multi-arts festival celebrating his work.
Her memoir,'Major/Minor', published last year, documents what life was like growing up in Paris in the 1980s.
In it she recounts how as a teenager, she didn't fully appreciate who her god-father was to the world.
"As a child I was more interested in actors and rock stars than writers," she explains.
"He used to come over for dinner.
"He was a very good friend of my father's. My father was a painter, my mother was a poet, so it was a very artistic relationship that they shared with Beckett. They would show each other their work, especially my father and Beckett.
"I would play the piano together with him. He would listen to a lot of music with my father and sometimes come in and listen to it too."
Alba started writing as a teenager and began sending some of her work to Beckett for his feedback.
"He would write back when he thought it was good and if he didn't like it he didn't write at all!" she says.
It was only at the age of 16 or 17 in school that she really discovered Beckett's catalogue of work.
"I remember we had coffee together when I was around 22, we had a proper conversation. I'm really glad we did that," says Alba, "He listened very carefully and talked about books, his experiences during the war and writing. I know I'm lucky I got to know him as I did."
Alba says her interest in Beckett now is purely a personal one.
"I'm not at all a Beckett expert. I know a lot of people who are coming to the festival are proper fans. I know his work a bit but I am not a total Beckett expert. I'm very pleased to be part of the festival of course. My mother wrote about him too. Her book, 'How it Was', is about his relationship with my father. It's a much more in-depth study because she was able to enjoy the friendship which lasted about 35 years."
Alba and her mother, Anne, will arrive in Enniskillen on Saturday.
It will be the first time she has ever stepped foot in Ireland.
"I'm very much looking forward to it. Beckett was a very inspiring man. Even when I was young, I felt that there was something very special about him -- he had a certain aura.
"But he was a shy man, very reserved. He didn't deal with publicity very well. I'm sure though, that he would be very pleased to know about the festival. He would have really appreciated it."