Spying module and mocking module function

I'm writing some tests for my component but I'm facing some troubles here...

Here is my Game component:

import React, { Component } from 'react';
import User from './user';
import Board from './board';

class Game extends Component {
  constructor(props) {
    super(props);
    this.board = new Board();
    //some more code
  }

  //some more code

  initializeUser(name) {
    const user = new User(name);
    //some more code

    user.pickCards();
    //some more code
  }

  //some more code

  render() {
    return (
      <div className="game-container">
      </div>
    );
  }
}

export default Game;

My Board component:

import React, { Component } from 'react';

class Board extends Component {
  constructor(props) {
    super(props);
    //some more code
  }

  //some more code
}

export default Board;

My User component:

import React, { Component } from 'react';

class User extends Component {
  constructor(props) {
    super(props);
    this.name = this.props.name;
    //some more code
  }

  //some more code

  pickCards() {        
    //some code
  }

  //some more code
}

export default User;

Now, at my tests I'm trying to test if the Board and User are called and if the pickCards() is called too.

Here are my tests:

import React from 'react';
import { mount } from 'enzyme';
import Game from './user';
import User from './user';
import Board from './board';

describe('Game start', () => {
  //some more code

  it('test 1', () => {
    //some code
  });

  it('test where I having problems', () => {      
    const boardSpy = jest.spyOn(Board, 'constructor'),
      userSpy = jest.spyOn(User, 'constructor'),
      pickCardMock = jest.fn();
    User.pickCard = pickCardMock;

    const wrapper = mount(<Game />, { attachTo: container });

    expect(boardSpy).toHaveBeenCalledTimes(1);
    expect(userSpy).toHaveBeenCalledTimes(1);
    expect(pickCardMock).toHaveBeenCalledTimes(1);
  });

  it('test 3', () => {
    //some code
  });
});

I don't want to mock Board and User because I need everything work normally on it. But I want to spy them to check if they were really called. And I want to mock pickCard().

I already tried to use jest.mock('./board'); and require('board') (for example) inside my test but it didn't work. And now I'm trying to spy the components constructors.

But the expect(boardSpy).toHaveBeenCalledTimes(1) fails saying that was called 0 times and not 1 time.

And the pickCardMock seems not being linked to the User module because when debugging pickCard is a normal function and not a mock function and expect(pickCardMock).toHaveBeenCalledTimes(1) receives 0 too instead of 1.

Anyone knows how to solve these two problems (spy a module and mock a function in the module)?