Well, the low speed fan kicks in on demand and runs when the relay is bypassed, so that's all dandy.
Nothing happens when you bypass the high speed fan at the engine fuse box, so I guess that's toast.
There is just one fan, low speed is achieved by using a huge resistor (which often burns out). If the low speed works then high should unless you have a wiring problem.
There's a hidden menu (like on BMW's) accessed via the odometer trip reset. Item 7 is the coolant temp in C. The low speed fan cuts in at 105C and brings the temp down. Only if you are really working the engine hard will you hit the 111C needed for the high speed fan.
In normal driving the fan often doesn't even come on at all, only when sitting in traffic.
If you use the hidden menu and you're not getting above 100C then there's a leak in the cooling system that's losing pressure, what happens then is the coolant boils and boils out of the reservoir. First thing to do here is replace the coolant pressure cap for about £13.