At a controlled field it's indeed ATC which opens or closes the flightplan, but it does help to check.
In the Netherlands, a flight plan is mandatory when departing or arriving at a controlled field, so plans are opened/closed by default. Also, flight plans are mandatory for international flight so if the controller knows that your destination is in another country, he will know that there is (or rather: should be) a plan in the system. But if in doubt, simply ask for confirmation.
At uncontrolled fields, it's your responsibility to close the flight plan. You typically walk to the C and ask them to phone the appropriate FIS to close the plan. Lots of fields ask your details over the radio upon first contact and once they know/suspect there's a flight plan in the system, they will call the FIS on their own accord as soon as you have landed successfully.
You can file a flight plan with Belgocontrol and they will distribute it for you to all relevant parties. If you're based in Belgium and normally use Belgocontrol, they will typically even assist you in filing a plan for a flight that happens to be outside Belgium. But otherwise you'll find that the airfield operator has a stack of ICAO forms which you can fill in, and they'll fax it to the appropriate FIS for filing.
So in short: At controlled fields there's typically a handling company, or a local flying club that's assisting you, and at uncontrolled fields there's typically an airfield operator. They can help you with all your flight planning needs.