The saga continues.
Replacement fan number 1 was reduced to scrap by trying to get the fan blade off. The screw moved a little (it's left hand thread) but then it stuck fast and wouldn't move either way. Very strange. Ended up welding a nut onto it but that just sheared the head off when we turned it. For curiosity we drilled the remains out, but the thing was clearly junk by this point.
So: try again.
This is replacement fan number 2. This time complete with loom.

Here's what's going on. There are four wires to the fan motor: two thick ones, a thinner one, and a thinnest one. They emerge from the plastic tubing behind the passenger side headlight.
One of the thick wires goes directly to earth. The other three continue up to the grey thing.
There are five wires to the grey thing: three from the fan, one to earth, and the white one goes to the black connector.
The one wire connector is clipped to the front of the battery box. I observe that this is the only external connection to the system, which I found very surprising -- a single wire supplies both power and 'control', but yet it's split up somehow before being sent down to the fan.
So what is this grey thing all about? Is it magic French electrical pixies?

It appears to be absent from the servicebox documentation where the fan loom has only two connections at its end.

I notice the pins are numbered 1, 2, 3, 5 (i.e., 4 is missing), and there are only 4 pins (also numbered 1, 2, 3, 5) where the loom attaches to the grey thing.
How the hell does this thing control a three speed fan?!
Anyway, I think this time I'll change the whole loom rather than risk messing up another fan by trying to get the fan blade off.