Enzyme was originally designed to work with Mocha, so getting it up and running with Mocha should be no problem at all. Simply install it and start using it:
npm i --save-dev enzyme
import React from 'react';
import { mount, shallow } from 'enzyme';
describe('<Foo />', () => {
it('calls componentDidMount', () => {
const wrapper = mount(<Foo />);
expect(Foo.prototype.componentDidMount.calledOnce).to.equal(true);
});
});