Sadly, there's no such neat service in the European area, but you can access some free charts (without flight plan overlay or something) here and there.
I think Eurocontrol offers some, with a free registration.

For planning along flight sim routes, I'm using Flight Sim Commander though, but this is payware and may distract you when starting as it has a rather old interface. There's a free trial available, just google it if you like.
FS Build may also be a tip there, the older 1.x version were freeware I think.

There are tons of features included in both and maybe the moving map helps on the first few runs. You can display and measure distances, bearings and so on and current nav data is also supported.
At least one more or less serious flight planning tool like these can be recommended in my eyes.

There are online services too, offering a free and a payware area, but I haven't tested those. Some work on a subscription basis, which I don't like much. But some planning features did sound good though, including maps and charts of all kind.