“The Frog and the Crocodile” was published in 1998, in an issue whose theme was private lives. This sounds fun, and it is. Beauvoir’s letters show a softer, surprisingly endearing side of the pioneering feminist, and Acocella mines them for the delightful and the dirty. The same formidable woman who produced “The Second Sex” and “The Ethics of Ambiguity” also declared herself Algren’s “own little love token,” enthusing over his “peculiar ways in boat-cabins” and erotic use of mirrors. Is it gossipy to examine such things in print? Maybe. But gossip has a legitimate purpose; it gives us human news. It’s also touching. With Algren, Beauvoir experienced sexual happiness for the first time. “Good for her,” Acocella writes, and she means it.