I am working on a project to combine React and Leaflet, but I must say I am having some hard time with the semantics.
As most of the stuff is managed by Leaflet directly
As an additional, less-detailed answer, PaulLeCam's react-leaflet component seems popular. Haven't used it yet but it looks promising:
https://github.com/PaulLeCam/react-leaflet
UPDATE: It's solid. Haven't used many of the features yet but the codebase is well-written and easy to follow and extend, and what I've used works great out of the box.