You can't go by color alone, you have to understand what the wires do. Here's what happened when you hooked all the like-colors together. BOOM.
This is probably how it was connected originally. However, this is wrong and illegal, for several reasons: white wires must be neutral unless marked otherwise, and here it's a hot mess. Also, "hot" is always connected to the light fixtures even with the switch off, which can surprise the guy working on the fixture. It's also likely that the white wires on the fixtures are actually "hot" - that's especially dangerous with Edison style sockets.
Here are the exact same wires, rearranged in a way which is legal and solves all of the above problems. Now the "hot" wire to the fixture (red) is switched, and neutral is always connected. With the switch off, the fixtures see no power. Note it now matters which end the switch is on, because on one end, white is actual-neutral, and on the other, it is switched-hot.
On the right of this drawing is called a switch loop. Those are wired with black-white cable out of sheer practicality... the white is not neutral, but is switched-hot. Legally the wire must be marked, typically with a few wraps of electrical tape. Black will suffice, use red if you have it.
This switch loop arrangement is actually obsolete. In new work, code now requires neutral be brought on switch loops. In that case, all 3 wires would be extended to the switch, and neutral would not be used until the happy day you get a smart switch or motion sensor.
The color of the wire-nuts do not matter, as long as they fit the wires - they have a lot of range. Yellow is best suited for all the connections here.
All these drawings omit ground wires. That's commonly done on illustrations like this. Nonetheless, all the grounds do need to be there and be hooked up.
One last thing: You'll get way less light. A dual 4-foot fluorescent (62-90 watts) produces the same light as 400-500 watts of tungsten bulbs. If you hate the fluorescent flicker, lousy cold-start or hum, or the ballast or starter has failed - electronic ballasts fix all that! And you can retrofit your existing fixtures. If you hate the fluorescent color, they fixed that too - tubes and LEDs now come in excellent color rendering (80-90 CRI) in 3000, 3500, 4000 or 5000k color.
Best Answer
Those are the modern European colors of brown=hot, blue=neutral and as always green=ground... Europe puts a yellow stripe on it.
All of these converge onto a 3-row terminal block, which is the usual method of interconnect in Europe. Note that all the wires to that terminal block enter the same side. That tells me the other side is intended for the external power connection. That's where you hook it up. There are screws to clamp the wire, looks like the screws are on the other side.
I assume the unit is meant to be permanently installed and hardwired. If you put a flexible cord-and-plug on it, make sure to have proper strain relief on the cord - preferably into a metal hole. The mounting area there is plastic and you could damage it with a hard yank on a cord.
The receptacle on the white part has nothing to do with supplying power to the unit. Once it is hooked up, this is a convenience outlet for small appliances, and appears to be the CEE 7/5 type common in Czech Republic, Austria and France. The ground may not work with other styles of Euro plugs, and you may be able to change the receptacle to a type more convenient to you.