The speed controller transistor module (some erroneously call it a resistor module because it is resistor instead of transistor on the manual instead of EATC), probably failed. It is on the firewall, right next to the fan, wire going from the fan to it.
They can fail from old age, or from overheating due to debris blocking the air passage or a fan on its way out and either way, not moving enough air to cool the module.
There's a DIY repair for the transistor on the module if you're good at soldering. It is the most likely problem, but there's also the possibility of bad wiring or connector(s), or the blower motor relay, instead of the transistor module, especially at this age of the vehicle. I could be mistaken but think possibly the blower motor relay is under the engine intake, air filter box. Hopefully someone will correct me if wrong.
See the wiring diagrams on this linked 1999 workshop manual PDF, section 55-1 page 150.
mega.nz
"IF" it is the fan speed controller, here are a couple part #'s to cross reference, though I'd just get an aftermarket one at around $30 rather than the more expensive motorcraft. F7SZ19E624AA, XL2Z19E624AA I'd get the speed controller at Rock Auto or Amazon but local auto parts stores used to carry them too and may still.
The problem could even be in the dash EATC head unit, so use the wiring diagram to see where power stops. The speed controller is what grounds the fan so if you were to jumper between the fan ground pin and a chassis ground and get the fan to work, this rules out wiring to it, and the relay, leaving wiring after it, the speed controller, and the head unit.
There is also a self diagnostic routine built into the head unit but I forget the key sequence to get it and pull its codes. There are other topics on this forum that should have that info and more about the EATC fan not working. I probably should have just linked to one of those topics instead of writing as much as I did.
All else fails, I also have the entire workshop manual section on HVAC diagnosis, but it is something also contained in the 2nd gen workshop manual linked in my sig, the first link on the post it links to instead of the one that I've linked above in this post.