Here's what Wikipedia has to say on this topic:
...both paternal and maternal grandfathers came directly from conversos, jews that converted in order to remain in the Iberian kingdoms or have access to posts in the Administration. And usually they carried a peculiar zeal in their new religion,in order to be confirmed and accepted by the christian community, preventing questioning (or Inquisition) about their identity, veracity of faith.
This post seems badly edited, so it may or may not be accurate. Some of you on this thread may know where to find the facts and edit the open-source posting on Wikipedia.
I think I wrote that his grandfather was the descendant of conversos. Many in Spain have conversos in their genealogical closet, probably most. His mother may have been part-jewish, ethnically, but she was a practicing Roman Catholic, as was his father. And since her name was Pilar, there must have been a Catholic in her family at least one generation back. Who knows? My best bet is that his converso ancestors converted early in the 19th century, when there was a lot of it going around. That said, during the German occupation of France, Franco allowed any French Jew who could get to the Spanish embassy in Paris to claim to be Spanish Sephardim, with a right to return to Spain, and supplied them with travel papers.