MFL (modern foreign language), although not compulsory, is taught at most British schools, and most certainly in private ones. The most common MFL is French.
Diana was first educated at Riddlesworth Hall which offers French as a core subject (key stage 1 and 2). Her next school was The New School at West Heath, which likewise offers an MFL as a core subject (key stage 3); Diana's MFL was French.
Diana was likely to have been fluent in French; in fact, I don't think I would be wrong to say most ladies of Diana's background could (and still can) speak French to varying degrees of fluency.