In reaction to the clarifications in the comments, I've greatly edited my question and tightened it a bit, including a fourth way of presenting dialogue and excluding references to the Portuguese 19th century novelist Eça de Queirós, with whose works the Free Indirect Speech is taught at High school.
I believe that you may be mixing narration and discourse techniques. I know Wikipedia states that "Free indirect speech is a style of third-person narration" in the opening sentence, but there are no sources for that statement and I'll try to explain why I believe it's false.
The way I see it, the narrator is an element of narrative while the dialogue (and all the ways of presenting it) is a mode of presenting text (I'm sorry, this is a very poor translation of the term I usually use in Portuguese). Therefore, they're two completely different things. That means they cannot be compared as 'peers'. One should first look at them separately and secondly see how they can work together.
First of all, there are four main ways of presenting dialogue in a novel:
direct speech
indirect speech
free direct speech
free indirect speech
- direct speech
"Hello," Charlie beamed as he joined the group. "I've aced the exam. The easiest thing in the world! I went in, spent two pens on miles long answers, and finished before everyone because every little detail was on the tip of the tongue. That is what proper studying does for you, guys!"
John rolled his eyes and sneered.
"You should wait for the results before gloating, Charlie."
The traditional approach. Gives rhythm and vitality, but can become boring when the dialogues become longer.
- indirect speech
Charlie joined the group with a boisterous hello, saying that he had aced the exam. He went on that it had been the easiest thing in the world! He had gone in, spent two pens on miles long answers, and finished before everyone because every little detail was on the tip of the tongue. But when he smuggly added that that was what proper studying did for folks, John rolled his eyes and sneered that he should wait for the results before gloating.
Avoids long dialogues but gives a sense of 'telling' rather than 'showing' when used too often.
- free indirect speech
Charlie joined the group with a boisterous hello, he'd aced the exam. The easiest thing in the world! He'd gone in, spent two pens on miles long answers, and finished before everyone because every little detail was on the tip of the tongue. That is what proper studying does for you, guys! John rolled his eyes with a sneer. He should wait for the results before gloating.
Again, it avoids long dialogues but it also diminishes the sense of 'telling' of the indirect speech since it feels a bit as if the reader is 'listening' to the actual speech.
- free direct speech
Charlie joined the group with a boisterous hello, the exam's been aced. The easiest thing in the world! Went in, spent two pens on miles long answers, and finished before everyone because every little detail was on tip of the tongue. That is what proper studying does for you, guys! John rolled his eyes with a sneer. Wait for the results before gloating, Charlie.
Note that free direct speech must be very close to the actual character's speech, without 'he' replacing 'I'. This makes the technique tricky in languages which require the subject to be always present, like English.
In Portuguese, on the other hand, the subject is not always necessary and, in a couple of verb tenses, the verb form for the first and third person singular is the same so this technique works like a charm, giving a lot of vitality and rhythm to the scene.
However, as the example shows, using free direct speech for long stretches can become awkward (in any language, though some are more tolerant). It's best to mix it with other techniques.
- direct speech + indirect speech + free direct speech + free indirect speech
Charlie joined the group with a boisterous hello, saying that he had aced the exam. The easiest thing in the world! He had gone in, spent two pens on miles long answers, and finished before everyone because every little detail was on the tip of the tongue. That is what proper studying does for you, guys! John rolled his eyes and sneered.
"Wait for the results before gloating, Charlie."
In the narration paragraph, mix indirect, free indirect and free direct speech (though you don't need the three at the same time). The vitality of the free speech will spice the basic indirect, but it won't become artificial. In English, it's best to use free direct only with exclamations and sentences which do not require personal pronouns when writing with a third-person narrator.
Since the question focuses on free indirect speech, I will now continue only with that technique for presenting dialogue and show how it can be used with all types of narrators (I'll go from the most to the least common).
third-person narrator
Sophie sneaked into the living room when Jack had his back to the door. Thankfully, she had no way of knowing he was talking to her brother. She sat behind the sofa, heart racing, as Jack said he'd had no way out. Julie knew everything, man! Should he have gone to prison because of her? Hell, no! And he'd do it again, damnit!
first-person narrator
I sneaked into the living room when Jack had his back to the door. Unfortunately, I hadn't heard the beginning of the conversation so I had no idea who he was talking to... perhaps he might still say their name. I sat behind the sofa, heart racing, as Jack said he'd had no way out. Julie knew everything, man! Should he have gone to prison because of her? Hell, no! And he'd do it again, damnit! How could I have loved that cold hearted man?
second-person narrator
You sneak into the living room when Jack has his back to the door. Unfortunately, you haven't heard the beginning of the conversation so you have no idea who he's talking to... perhaps he might still say their name. You sit behind the sofa, heart racing, as Jack says he'd had no way out. Julie knew everything, man! Should he have gone to prison because of her? Hell, no! And he'd do it again, damnit! How could you have loved that cold hearted man?
In conclusion, free indirect speech is used to present the voices of the characters. If that voice is spoken (actual spoken dialogue or monologue), it makes no difference who the narrator is because FIS can be used. However, FIS cannot be used to convey the thoughts of a first-person narrator (or a second-person narrator), but that is a limitation of the technique.