It’s definitely canon that Joly and Bossuet have both been involved with Musichetta, and that Joly and Bossuet live together more often than not, and are in general Partners. From Preliminary Gayeties (4.12.2, Hapgood Edition):
Laigle de Meaux, as the reader knows, lived more with Joly than elsewhere. He had a lodging, as a bird has one on a branch. The two friends lived together, ate together, slept together. They had everything in common, even Musichetta, to some extent. They were, what the subordinate monks who accompany monks are called, bini.
And of course it’s established way back in 3.4.4 that Joly and Musichetta are An Item! Hugo never specifies their relationship beyond that; you can headcanon a full-on poly trio, Musichetta being on-again-off-again with both of them, Musichetta having dated one or the other of them first, both of them having dated her at some point before realizing that actually they’re just gay together, whatever. Current LM Fandom (and I very much include myself in this) has generally settled on the obvious poly reading.
If you were to pin me down and ask me under duress what I think Hugo Really Intended in full cultural context…? Honestly, I’d hazard that he intends them to be an established Relationship Triad. And probably one with minimal drama about it! Like, really-really, that would be my honest cultural-context-based, broader-reading supported interpretation. But I do think Hugo was probably thinking of the three of them according to a specific formulation that would have been recognized as a pretty Standard Trope by his readers.
I mean, it’s a story about oppression and the evils of the world, a story about the downtrodden, the mistreatment of people at the hands of the government and society…
…Any idea why trans/nb/gnc people might feel drawn to that?
¯_( ಠ_ಠ)_/¯ 