I got a nerdy and freaky similarity: Les Misérables VS Lord of the Rings
The battle at the barricade is similar to Helm´s Deep, because both are battles where the "good" side is sorrounded and outnumbered.
Jean Valjean in the sewers carrying Marius is like Samsagaz in Mordor carrying Frodo. Thenárdier is a doorman as Gollum is a guide.
Besides, there are more similarities between Thenárdier and Gollum, but the main similarity is that, being bad people, both have a providential role in the end.
Gillenormand/Denethor, and his attitude towards Marius/Faramir.
Tolkien´s physical description of Moria reminds me of Hugo´s moral descriptions of the society depths.
Nazguls are multiplied sosias of Javert, as they are hunters, whereas the Ring can be a metaphor of the Guilt, both the internal of Valjean as the guilt before the justice Javert want to fullfill.
May look rare, but Boromir looks me like Éponine, since he is a rude character who finally sacrificates himself for something he feels as precious, just like Éponine.
Tom Bombadil looks like a kind of Gavroche. Both are happy and lords of their little kingdoms.
Hobbiton is a kind of Montreuil-sur-Mer. Quiet and happy places from where the main character has to go in order to fullfill a mission.
Fellowship of the Ring, specially hobbits, loosely inspired in the ABC friends, with Frodo as Marius, Aragorn as Enjolras, and Pippin as Grantaire.
Myriel and Gandalf, both of them make a change on the main character at the beginning.
The sense of Loss in both works, reflected mainly in the change from Fantine´s happy era/Middle Land´s Golden Age, to both ends.
Tolkien´s metaphor of the Hobbits, little people, symbolizing the poor people. Even the littlest one can be a hero/even a poor one between the poor ones can be a hero (Valjean).
I am sure that more similarities can be found.