The simplest answer is just to move Home into the render() method of your app, like so:
class App extends Component {
    render() {
        return (
            <Home />
        );
    }
}
Then, in your routes at the top, you could just have this: 
<Router>
  <div>
    <Route exact path="/" component={App}/>
    <Route path="/Project" component={Project}/>
  </div>
</Router>
However, it depends on what you want to do, exactly. Does the App always have Home as a child component? Otherwise, you can nest your inner component within the router like so:
  
    
      
      
    
  
This would set the props.children of the App to be the specific component that you are trying to use. That could be then used within your App like so:
class App extends Component {
    render() {
        return (
            <MyHeaderComponent />
            {this.props.children}
            <MyFooterComponent />
        );
    }
}