[cracks knuckles]
-Okay, as
Scrounge notes, you're not supposed to have any switches or breakers between the VFD and the motor. Switching a VFD output under load can blow out the electronics- newer VFDs are supposed to be more resistant, but you're still not supposed to do it.
Now, that said, I have an Arboga gear-head drill press, that has a built-in 2-speed motor. It originally came wired for native 3-phase, and so had a rotary switch: hi-off-low.
As I was going to run it off a VFD, what I did was repurpose the original switch and mount it in the side of the casting. It still works the same way, but using the VFD feed.
Since I am the only one that will ever be using it, I simply make sure the VFD is off (that is, not currently powering the motor, not, like, "powered down" off) before I switch from high to low or vice-versa.
I then have some low-voltage buttons on the front of the machine for conventional start/stop, controlling the VFD itself.
An alternative is, as suggested above, to wire just one of the windings sets, and simply always run the drill on either high speed (say, for woodworking) or low speed (for metalworking.)
Keeping in mind that a good VFD can indeed slow down a fast setting, but at the same time you lose HP as fast as you lose RPM. And trying to turn a big drill in steel needs to be very slow AND have lots of torque. You won't get that just letting the VFD slow the motor down.
AND... something I just learned on a lathe I've been working on, there are in fact 2-speed motors that
cannot be run- at least not well, or for long- on just one 'winding'.
My lathe has a 2-speed that's apparently called a "concurrent pole" motor- as I understand it (and my understanding is thin

) it's something like wiring it in wye gets one speed, and wiring it in delta gets the other speed.
And in one or the other, two fields, I think, need to be shorted.
That setup pretty much had to be run on native 3-phase, no VFD was going to do the job, without some seriously fancy wiring, plus relays and whatnot. As it was, just wiring the correct style of breakers took no small bit of doin'.
So yes, I'd say you need to dig up a proper diagram for that motor, and make sure that you actually can run it off a VFD.
Or grab/build a small rotary converter and feed it proper(ish) 3-phase. That's what I had to do for my lathe.
Doc.