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 { expect } from 'chai';
import { mount } from 'enzyme';
import { spy } from 'sinon';
import Foo from './src/Foo';
spy(Foo.prototype, 'componentDidMount');
describe('<Foo />', () => {
it('calls componentDidMount', () => {
const wrapper = mount(<Foo />);
expect(Foo.prototype.componentDidMount).to.have.property('callCount', 1);
});
});