It is the best guarded secret in Belgian history, nobody knows for sure.
According to Cardinal Seuens, he arranged the match, he was simply looking for a devout young noble woman, sent Sister Veronica O'Brien out to Spain, where she met up with the Head of a school who knew Fabiola. According to this story, Sister O'Brien had a vision of a painting of the Virgin Mary. When she met with Fabiola at her appartment in Madrid, she saw that same painting at a wall in the appartment, and she knew Fabiola would be the one.
However, photographic evidence suggests they knew each other for a few years before the engagement, this would contradict the above story in timeline.
It is also possible the match happened at Queen Ena's in Switzerland, while Fabiola was accompanying one of her granddaughters (for whom the match was originally intended).
Other story claims that they met at a party in Madrid, but Fabiola didn't recognize him, as he was not wearing his glasses. They fell in love there and managed to keep it a secret for many years before their engagement.
It is said that she accepted his marriage proposal on a holiday in Lourdes, while they were driving towards Tarbes, after having refused him a couple of times.
In reality, even though Seuens' story seems plausible enough, the only people who know if it's true are King Boudewijn and Queen Fabiola, and I don't think either is going to tell.