If you are using MVVM pattern, you do not need Click event at all.
You should use MenuItem.Command property in order to communicate with your ViewModel.
HOW?
As I can see, you are using the ItemContainerStyle. You can add the following line to that style:
<Style x:Key="RecentMenuItem" TargetType="MenuItem">
...
<Setter Property="Command" Value="{Binding Path=SelectCommand}" />
...
</Style>
And in your RecentFile
:
public ICommand SelectCommand { get; private set; }
You can initialize the command inside the constructor of RecentFile
class.