The Motobecane is a Mirage. If I were to do a build, I wouldn't need to replace the fork, headset, stem, handlebars, or bb (even though it's probably a good idea to do so) so essentially even though the I would be getting a new BB it wouldn't have to fit.

That being said I wouldn't call it rideable at this point:
The rear brake cable snapped off the hood after pulling too hard
The chainring is bent, as is the front derailleur (limiting it to 5 gears)
The chain falls off on the smallest cog (limiting it to 4 gears)

So if I don't build it, it's going on CL as a "Vintage" (ooo!) bike.

That being said it appears that there's no clear consensus as to which is a better idea.

Right now I'm leaning towards the build because as someone said you can always get a better frame and but the parts on that.

But please, continue!