PARIS—As police intelligence agents in Paris tracked Islamist radicals over the summer, one of their longtime colleagues was quietly embracing a more extreme version of his Muslim faith. While away from the office, Mickaël Harpon, a 45-year-old convert to Islam, had begun dressing in more religious garb and established ties with followers of Salafism, a fundamentalist strain of Islam, according to prosecutors. At work, he appeared to avoid physical contact with women, colleagues would later tell prosecutors. During his lunch break last week, Harpon bought two knives, returned to the office and stabbed four of his colleagues to death. He...