Looks like you haven’t loaded in the Leaflet stylesheet.

From the react-leaflet GitHub guide:

If you are not familiar with Leaflet, make sure you read its quick start guide before using this library.
You will notably need to add its CSS to your page to render the map properly, and set the height of the container.

http://leafletjs.com/examples/quick-start/

Here is what you’ll need:

<link rel="stylesheet" href="https://unpkg.com/leaflet@1.0.1/dist/leaflet.css" />

Update

Note @ThomasThiebaud indicates you may also have to set up the height of .leaflet-container

—

Ange Loron also gave a correct, optional, JS module import (vs cdn or style link)

import 'leaflet/dist/leaflet.css';

For what its worth, the documentation page is poorly designed… and the maintainer continuously deals with this issue in GitHub, but for some reason, the issue is the *fault of the users who continuously don’t do the required setup. /s