"Indirect libre" is the French term for "free indirect discourse," which is a narrative technique that developed around the turn of nineteenth century (in English-language literature, its origin is heavily associated with Jane Austen). Free indirect discourse is a kind of middle ground between first and third person narration; it involves a third-person narrator reporting a character's thoughts (or sometimes speech) without explicitly saying that he's doing so. For that reason, free indirect discourse also tends to blur the lines between the narrator and his characters, because our access to the characters' thoughts and feelings depends on the "translation" provided by the narrator.
Flaubert used free indirect discourse extensively in his novels, and his work helped popularize the technique. There is no shortage of examples in Madame Bovary, but here is a particularly clear one from chapter 8:
The next day was a long one. She walked about her little garden, up and down the same walks, stopping before the beds, before the espalier, before the plaster curate, looking with amazement at all these things of once-on-a-time that she knew so well. How far off the ball seemed already! What was it that thus set so far asunder the morning of the day before yesterday and the evening of to-day? Her journey to Vaubyessard had made a hole in her life, like one of those great crevices that a storm will sometimes make in one night in mountains. Still she was resigned. She devoutly put away in her drawers her beautiful dress, down to the satin shoes whose soles were yellowed with the slippery wax of the dancing floor. Her heart was like these. In its friction against wealth something had come over it that could not be effaced.
Notice that Flaubert doesn't explicitly say "Emma thought, 'How far off the ball is already!'" but instead uses other cues (e.g., the exclamation mark) to clarify that we are inside Emma's head. Notice also, though, that it's hard to pinpoint exactly when we revert to the narrator's voice: is Flaubert, for instance, simply reporting that Emma "was resigned," or is Emma herself conscious of being "resigned"?