Valérie Trierweiler faces an uncommon predicament. Twice married and twice divorced, she covered French politics as a journalist for more than 20 years with no inkling that she would one day become France’s first lady, certainly not when she fell for François Hollande, a jovial, unglamorous leftist politician who hardly seemed like presidential material. “I almost want to laugh when I think of it,” Ms. Trierweiler said in a telephone interview. But Mr. Hollande was elected on May 6 and was sworn in on Tuesday, and now Ms. Trierweiler — whom he calls “the love of my life” — is...