Have any of you bothered to learn about the FUNCTIONS of MBTI? Without the functions, the four letters are MEANINGLESS. That's why people make the mistake of saying things like "sometimes I'm INFJ and sometimes, I'm INFP" Even though those two personality types have NOT A SINGLE FUNCTION in common. It's more than just Feeling/Thinking, iNtuition/Sensing, Perceiving/Judging, and Introversion/Extroversion. It's Fi/Fe, Ti/Te, Ni/Ne, Si/Se and the order of preference with which they prefer to use them. Fi, Ne, Si Te? INFP. Ni Fe Si Te? INFJ. FeNiSeTi? ENFJ. SeTiFeNi? ESTP. NeTiFeSi? ENTP. TeSiNeFi? ESTJ. SiTeFiNe? ISTJ. Etc. etc. So it's important to remember the FUNCTIONS and try to understand them well, or MBTI is meaningless. (Although some skeptics argue that MBTI is meaningless anyway, but that's another argument)
I believe in the movie, Gavroche is an ENFP. He's DEFINITELY an Extroverted Perception dominant and and I'm guessing he's more Fi than Ti auxilliary, so that leaves ESFP and ENFP. In the movie, whether parroting arguments from the scholars (more likely) or drawing the connections himself (more impressive, but less likely for a boy that age) he still shows a pretty good understanding of the basic concepts behind the scholars' beliefs in his movie version of the song (it's more detailed in his movie version describing the failure of the revolution) and he thusly displays enough interest in the concepts themselves to have picked up on them at such an early age despite being poor and likely, uneducated (outside of what the scholars teach. Or at least, not very WELL educated)
However, the play version seems less conceptual, so I'm going with ESFP there, cause he usually displays quite a bit of physical energy with his performance (Extroverted Sensing)
As for Javert? Either ESTJ or ISTJ. Hard to tell. Maybe ISTJ, because with inferior Ne, they're known to be pretty inflexible (think Hank Hill, ISTJ mascot) On the other hand, He could be Fi inferior with his mercilessness. But Fi is not always kind hearted. Being introverted in nature, if not properly developed, It can be very self-oriented and dogmatic. Hard to tell with JAvert, but he's definitely one of the two.
Thernardier seems to be ENTP or ESTP. I'm thinking ESTP. His goals are always fairly simple, straight-forward and singleminded (inferior Ni?): Sex, Survival, Money, Luxury if he could get it, flashy things, such as the ring he stole from Marius and kept as a souvenir (all Se oriented) And he seems Ti auxilliary, so there's that...
As for Éponine, she's got so many problems and seems so unhealthilly developed, that it's hard to say for sure her type. ENFP seemed pretty good to me, though. She was intuitive enough (N) and in touch with her own emotions enough (Fi) that she was able to realize it wasn't really Marius she was in love with, but the idea of him. The fact that she decided to still entertain this fantasy, KNOWING it was unfullfillable and bullshit anyway, just to have something in her life (almost like an escape, similar to Cossette's castle in the clouds) kinda suggests Ne dominance.