I'm overhauling a Motobecane Nomade for someone, and at one point it was upgraded with a new BB and a cotterless crankset. When I went to remove the fixed cup, it wouldn't budge. I know they're supposed to be in really tight, but I've never failed to get one out...anyway, I let it go. When I went to remove the adjustable cup, though, it too wouldn't budge. If I try any harder I'm going to snap my BB tool. But here's the thing...the lockring spun right off, and the grease on the threads is still fresh...so the cups were greased, and it wasn't in the too distant past either. My guess is that someone shoved a BB in with the wrong threading...problem is they didn't even bother to get the adjustment right Any other thoughts on what could be going on, or is that probably it?

Might be cross-threaded. If it's French thread, an English thread cup will go in on the left but not the right. So if they match they are probably the right cups.

Try taking a small drift that will fit in the holes of the adjustable cup and tap loose with a hammer. Heating it with a propane torch and letting it completely cool first will help as well (on both sides).

Which way are you turning it? If you're assuming French and RH thread on both sides you may be wrong, Motos are often Swiss threaded, adjustable RH, but fixed cup LH like an English BB, but with french size/pitch threading. If they stuffed an english BB in a french/swiss shell, it still should come loose as 1.37" = 34.8mm, french/swiss is 35.0. Butchered but still should come out. You have the lockring off - do you have another BB as a reference that it will thread onto?

I was trying the fixed cup as if it were French threading, but regardless the adjustable cup won't move. The worst adjustable cup I've ever had to unscrew was still "easy"...this one is seriously frozen. And your post made me think to actually clean off the faces and look at the threading (duh)...which is 1.37. They're Shimano cups. The lockring threads onto Japanese adustable cups just fine. Loctite maybe?

Sounds like a good guess. Time for a bigger wrench and/or torch. Hopefully they used the blue and not the red.

If they red loctite-d it then the torch is what you need, cause red loctite needs HEAT to soften enough to unscrew...but I think you just need a "bigger hammer" such as a big bolt/bunch of lock washers/nut and two sockets/wrenches with a big washer to hold your wrench on the fixed cup and...a dead blow mallet...works every time!